CECCO Namespace Reference

Provides a framework for error correcting codes. More...

Namespaces
namespace	details
	Contains implementation details not to be exposed to the user. Functions and classes here may change without notice.

Classes
class	SDMEC
	Symmetric errors-and-erasures channel over a finite field. More...
class	SDMC
	Symmetric Discrete Memoryless Channel: errors only, no erasures. More...
class	BEC
	Binary Erasure Channel: symbols are received correctly or marked erased. More...
class	BAC
	Binary Asymmetric Channel (Z-channel): 0 is preserved; 1 flips to 0 with probability p. More...
class	NRZMapper
	Non-Return-to-Zero (NRZ) mapper for binary modulation. More...
class	BPSKMapper
	Binary Phase Shift Keying mapper: NRZMapper with a = 0, b = 2. More...
class	AWGN
	Additive White Gaussian Noise channel for complex-valued symbols. More...
class	BI_AWGN
	Binary-Input AWGN: fused NRZMapper + AWGN block. More...
class	NRZDemapper
	Non-Return-to-Zero (NRZ) hard-decision demapper. More...
class	BPSKDemapper
	BPSK hard-decision demapper: NRZDemapper with threshold 0. More...
class	LLRCalculator
	Compute symbol-level log-likelihood ratios. More...
class	DEMUX
	Expand extension-field elements into subfield coordinates. More...
class	MUX
	Field multiplexer: reconstruct 𝔽_E elements from 𝔽_S coefficients. More...
class	Code
class	EmptyCode
class	LinearCode
class	UniverseCode
class	ZeroCode
class	SimplexCode
class	SingleParityCheckCode
class	ExtendedCode
class	CodewordIterator
class	decoding_failure
class	HammingCode
class	RepetitionCode
class	GolayCode
class	GRSCode
class	RSCode
class	CordaroWagnerCode
class	ConvolutionalCode
class	LDCCode
class	RMCode
class	SubfieldSubcode
class	AlternantCode
class	BCHCode
class	GoppaCode
class	AugmentedCode
class	Enc
class	Dec
class	Dec_list
class	ListProcessor
class	Encinv
class	Rationals
	Field of rational numbers ℚ = { p/q : p, q ∈ ℤ, q ≠ 0 } with selectable precision. More...
class	Polynomial
	Univariate polynomial p(x) = a₀ + a₁x + … + aₙxⁿ over a CECCO::CoefficientType. More...
class	Fp
	Prime field 𝔽_p ≅ ℤ/pℤ More...
class	Ext
	Extension field 𝔽_{q^m} ≅ B[x]/(f(x)), constructed from a base field and an irreducible monic modulus polynomial. More...
class	Iso
	Single logical field unifying several pairwise-isomorphic representations. More...
class	Vector
	Vector v = (v₀, v₁, …, vₙ₋₁) over a CECCO::ComponentType. More...
class	Matrix
	Dense m × n matrix over a CECCO::ComponentType. More...
class	Embedding
	Functor representing the field embedding φ: SUBFIELD → SUPERFIELD, with reverse lookup. More...
class	Isomorphism
	Functor representing the field isomorphism φ: A → B between two same-size finite fields. More...
struct	Trellis
	Layered trellis with field-labelled edges. More...
struct	TannerGraph
	Tanner graph of a parity-check matrix. More...
class	RNG
	Thread-local random number generator with shared seeding policy. More...
class	SierpinskiTriangle
	Sierpinski triangle (Pascal's triangle modulo p). More...

Concepts
concept	FieldType
	Concept for field types: full algebraic interface.
concept	FiniteFieldType
	Refines FieldType for finite fields 𝔽_{p^m}.
concept	SignedIntType
	Standard signed integers or InfInt for arbitrary precision.
concept	CoefficientType
	Admissible coefficient type for CECCO::Polynomial (scalar-like types).
concept	PolynomialType
	T is a Polynomial<C> over some CoefficientType C.
concept	ReliablyComparableType
	Types whose operator== reflects mathematical equality.
concept	ComponentType
	Admissible component type for CECCO::Vector and CECCO::Matrix.
concept	BelongsTo
	T is identical to at least one of Types....
concept	Isomorphic
	A and B are finite fields of the same size (and thus isomorphic).
concept	SubfieldOf
	SUBFIELD ⊆ SUPERFIELD as constructed in this library (Iso paths included).
concept	ExtensionOf
	Inverse of SubfieldOf: ExtensionOf<S, E> iff SubfieldOf<E, S>.

Typedefs
using	BSC = SDMC<Fp<2>>
	Binary Symmetric Channel: type alias for SDMC<Fp<2>>.
template<class B>
using	base_t = std::remove_cvref_t<B>
template<class C>
using	field_t = typename base_t<C>::FIELD
template<uint16_t p, uint8_t m = 1>
using	label_t = typename std::conditional_t<sqm(p, m) < 255, uint8_t, uint16_t>

Enumerations
enum class	method_t {   BD , standard_array , BD_standard_array , boosted_BD_standard_array ,   ML , ML_soft , Viterbi , Viterbi_soft ,   BCJR , ssMAP , BP , recursive ,   Meggitt , WBA , WBA_optimized , BMA ,   OSD , LC_OSD , WBA_EE , BMA_EE ,   BD_EE , ML_EE , Viterbi_EE , recursive_EE ,   GMD }
enum class	list_method_t {   Viterbi , Viterbi_soft , SA , SA_optimized ,   GSA , GSA_optimized , KVA }
enum class	list_processing_t { pick_first , pick_random }
enum class	termination_t { zero_terminated , tailbitten }
enum class	LutMode { CompileTime , RunTime }
	LUT generation mode for field operations. More...

Functions
	LLRCalculator (const NRZMapper &, const AWGN &) -> LLRCalculator< Fp< 2 > >
	LLRCalculator (const BI_AWGN &) -> LLRCalculator< Fp< 2 > >
template<FiniteFieldType T>
	LLRCalculator (const SDMEC< T > &) -> LLRCalculator< T >
template<class LHS, class RHS>
decltype(auto)	operator>> (LHS &&lhs, RHS &&rhs)
	Function-call chaining: x >> f ≡ f(x).
template<class LHS, class RHS>
RHS &	operator>> (LHS &&lhs, RHS &dst)
	Assignment chaining: x >> dst ≡ dst = x; return dst.
template<FiniteFieldType T>
long double	HammingUpperBound (size_t n, size_t dmin)
template<FiniteFieldType T>
long double	JohnsonUpperBound (size_t n, size_t dmin)
template<FiniteFieldType T>
long double	PlotkinUpperBound (size_t n, size_t dmin)
template<FiniteFieldType T>
long double	EliasUpperBound (size_t n, size_t dmin)
size_t	SingletonUpperBound (size_t n, size_t dmin)
template<FiniteFieldType T>
size_t	GriesmerUpperBound (size_t n, size_t dmin)
template<FiniteFieldType T>
long double	UpperBound (size_t n, size_t dmin)
template<FiniteFieldType T>
size_t	GilbertVarshamovLowerBound (size_t n, size_t dmin)
template<FiniteFieldType T>
size_t	BurstUpperBound (size_t n, size_t ell)
constexpr size_t	ReigerBurstUpperBound (size_t n, size_t ell)
template<FiniteFieldType T>
Polynomial< InfInt >	MacWilliamsIdentity (const Polynomial< InfInt > &A, size_t n, size_t k)
std::ostream &	showbasic (std::ostream &os)
std::ostream &	showmost (std::ostream &os)
std::ostream &	showall (std::ostream &os)
std::ostream &	showspecial (std::ostream &os)
template<class B>
	SubfieldSubcode (const B &) -> SubfieldSubcode< B >
template<class B>
	SubfieldSubcode (B &&) -> SubfieldSubcode< B >
template<FieldType T>
auto	dual (const LinearCode< T > &C)
template<class B>
auto	extend (B &&base, size_t i, const Vector< field_t< B > > &v)
template<class B>
auto	extend (B &&base)
template<FieldType T, class B>
B	unextend (const ExtendedCode< T, B > &C)
template<class B>
auto	augment (B &&base, size_t j, const Vector< field_t< B > > &w)
template<FieldType T, class B>
B	unaugment (const AugmentedCode< T, B > &C)
template<class B>
auto	lengthen (B &&base, size_t j, const Vector< field_t< B > > &w, size_t i, const Vector< field_t< B > > &v)
template<class B>
auto	lengthen (B &&base, size_t j, const Vector< field_t< B > > &w)
template<FieldType T, class D>
auto	unlengthen (const ExtendedCode< T, AugmentedCode< T, D > > &C)
template<FieldType T>
LinearCode< T >	puncture (const LinearCode< T > &C, const std::vector< size_t > &v)
template<FieldType T>
EmptyCode< T >	puncture (const EmptyCode< T > &, const std::vector< size_t > &)
template<class C>
auto	puncture (C &&code, size_t i)
template<FieldType T>
LinearCode< T >	expurgate (const LinearCode< T > &C, const std::vector< size_t > &v)
template<FieldType T>
EmptyCode< T >	expurgate (const EmptyCode< T > &, const std::vector< size_t > &)
template<class C>
auto	expurgate (C &&code, size_t j)
template<class B>
auto	shorten (B &&base, size_t j, size_t i)
template<FieldType L, FieldType R>
bool	operator== (const LinearCode< L > &lhs, const LinearCode< R > &rhs)
template<FieldType L, FieldType R>
bool	operator!= (const LinearCode< L > &lhs, const LinearCode< R > &rhs)
template<FieldType L, FieldType R>
bool	identical (const LinearCode< L > &lhs, const LinearCode< R > &rhs)
template<FieldType L, FieldType R>
bool	equivalent (const LinearCode< L > &lhs, const LinearCode< R > &rhs)
template<FieldType T>
std::ostream &	operator<< (std::ostream &os, const Code< T > &rhs)
template<SignedIntType T>
std::ostream &	operator<< (std::ostream &os, const Rationals< T > &e)
	Print as "numerator/denominator" (or just "numerator" when denominator is 1).
template<uint16_t p>
std::ostream &	operator<< (std::ostream &os, const Fp< p > &e)
	Print as the integer label (or ERASURE_MARKER if erased).
template<FiniteFieldType B, MOD modulus, LutMode mode>
std::ostream &	operator<< (std::ostream &os, const Ext< B, modulus, mode > &e)
	Print as the integer label (or ERASURE_MARKER if erased).
template<FieldType T>
std::ostream &	operator<< (std::ostream &os, const Trellis< T > &Tr)
std::mt19937 &	gen ()
	Current thread's random number generator.
template<class T>
std::vector< size_t >	find_maxima (const std::vector< T > &v)
	Indices of all maximum elements.
template<class T>
constexpr bool	is_prime (T a) noexcept
	Primality test by trial division.
template<class T>
constexpr T	GCD (T a, T b, T *s=nullptr, T *t=nullptr)
	Greatest common divisor and optional Bézout coefficients.
template<uint16_t p, class T>
constexpr T	modinv (T a)
	Multiplicative inverse modulo a prime.
template<class T>
T	fac (T a)
	Factorial a!
template<class T>
T	bin (const T &n, T k)
	Binomial coefficient C(n,k).
template<>
InfInt	bin (const InfInt &n, InfInt k)
	Binomial coefficient specialization for InfInt.
long double	log2 (const InfInt &v)
	Base-2 logarithm of a positive InfInt of arbitrary magnitude.
long double	to_long_double (const InfInt &v)
	Conversion of an InfInt of arbitrary magnitude to long double.
template<class T>
constexpr T	sqm (T b, int e)
	Exponentiation by square-and-multiply.
template<class T>
constexpr T	daa (T b, int m)
	Scalar multiplication by double-and-add.
template<ComponentType T>
constexpr Matrix< T >	ZeroMatrix (size_t m, size_t n)
	m × n matrix of zeros (tag details::Zero)
template<ComponentType T>
constexpr Matrix< T >	IdentityMatrix (size_t m)
	m × m identity matrix I_m
template<ComponentType T>
constexpr Matrix< T >	DiagonalMatrix (const Vector< T > &v)
	Diagonal matrix with diagonal v (strongest tag of details::Zero, details::Identity, details::Diagonal).
template<ComponentType T>
constexpr Matrix< T >	ToeplitzMatrix (const Vector< T > &v, size_t m, size_t n)
	m × n Toeplitz matrix from its diagonal entries
template<ReliablyComparableType T>
constexpr Matrix< T >	VandermondeMatrix (const Vector< T > &v, size_t m)
	Vandermonde matrix V_{i, j} = v[j]^i.
template<ComponentType T>
std::ostream &	operator<< (std::ostream &os, const Matrix< T > &rhs)
	Pretty-print the matrix with column alignment and bracket borders.
template<ComponentType T>
constexpr Matrix< T >	operator+ (const Matrix< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator+ (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator+ (const Matrix< T > &lhs, Matrix< T > &&rhs)
template<ComponentType T>
constexpr Matrix< T >	operator+ (Matrix< T > &&lhs, Matrix< T > &&rhs)
template<ComponentType T>
constexpr Matrix< T >	operator- (const Matrix< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator- (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator- (const Matrix< T > &lhs, Matrix< T > &&rhs)
template<ComponentType T>
constexpr Matrix< T >	operator- (Matrix< T > &&lhs, Matrix< T > &&rhs)
template<ComponentType T>
constexpr Matrix< T >	operator* (const Matrix< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator* (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	operator* (const Vector< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	operator* (Vector< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator* (const Matrix< T > &lhs, const T &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator* (Matrix< T > &&lhs, const T &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator* (const T &lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator* (const T &lhs, Matrix< T > &&rhs)
template<CoefficientType T>
constexpr Matrix< T >	operator/ (const Matrix< T > &lhs, const T &rhs)
template<CoefficientType T>
constexpr Matrix< T >	operator/ (Matrix< T > &&lhs, const T &rhs)
template<CoefficientType T>
Matrix< T >	randomize (const Matrix< T > &M)
template<CoefficientType T>
Matrix< T >	randomize (Matrix< T > &&M)
template<ReliablyComparableType T>
constexpr size_t	wH (const Matrix< T > &M)
template<ReliablyComparableType T>
size_t	dH (const Matrix< T > &lhs, const Matrix< T > &rhs)
	Hamming distance dₕ(lhs, rhs) = wₕ(lhs − rhs).
template<ReliablyComparableType T>
size_t	dH (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ReliablyComparableType T>
size_t	dH (const Matrix< T > &lhs, Matrix< T > &&rhs)
template<ReliablyComparableType T>
size_t	dH (Matrix< T > &&lhs, Matrix< T > &&rhs)
template<ComponentType T>
Matrix< T >	set_component (const Matrix< T > &M, size_t i, size_t j, const T &c)
template<ComponentType T>
Matrix< T >	set_component (Matrix< T > &&M, size_t i, size_t j, const T &c)
template<ComponentType T>
Matrix< T >	get_submatrix (const Matrix< T > &M, size_t i, size_t j, size_t h, size_t w)
template<ComponentType T>
Matrix< T >	set_submatrix (const Matrix< T > &M, size_t i, size_t j, const Matrix< T > &N)
template<ComponentType T>
Matrix< T >	set_submatrix (Matrix< T > &&M, size_t i, size_t j, const Matrix< T > &N)
template<ComponentType T>
Matrix< T >	horizontal_join (const Matrix< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	horizontal_join (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	horizontal_join (Matrix< T > &&lhs, Matrix< T > &&rhs)
template<ComponentType T>
Matrix< T >	vertical_join (const Matrix< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	vertical_join (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	vertical_join (Matrix< T > &&lhs, Matrix< T > &&rhs)
template<ComponentType T>
Matrix< T >	diagonal_join (const Matrix< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	diagonal_join (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	diagonal_join (Matrix< T > &&lhs, Matrix< T > &&rhs)
template<ComponentType T>
Matrix< T >	Kronecker_product (const Matrix< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	Kronecker_product (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	Kronecker_product (Matrix< T > &&lhs, Matrix< T > &&rhs)
template<ComponentType T>
Matrix< T >	swap_rows (const Matrix< T > &M, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	swap_columns (const Matrix< T > &M, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	swap_rows (Matrix< T > &&M, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	swap_columns (Matrix< T > &&M, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	scale_row (const Matrix< T > &M, const T &s, size_t i)
template<ComponentType T>
Matrix< T >	scale_column (const Matrix< T > &M, const T &s, size_t i)
template<ComponentType T>
Matrix< T >	scale_row (Matrix< T > &&M, const T &s, size_t i)
template<ComponentType T>
Matrix< T >	scale_column (Matrix< T > &&M, const T &s, size_t i)
template<ComponentType T>
Matrix< T >	add_scaled_row (const Matrix< T > &M, const T &s, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	add_scaled_column (const Matrix< T > &M, const T &s, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	add_scaled_row (Matrix< T > &&M, const T &s, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	add_scaled_column (Matrix< T > &&M, const T &s, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	add_row (const Matrix< T > &M, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	add_column (const Matrix< T > &M, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	add_row (Matrix< T > &&M, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	add_column (Matrix< T > &&M, size_t i, size_t j)
template<ComponentType T>
constexpr Matrix< T >	delete_columns (const Matrix< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	delete_columns (Matrix< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	delete_column (const Matrix< T > &lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	delete_column (Matrix< T > &&lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	delete_rows (const Matrix< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	delete_rows (Matrix< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	delete_row (const Matrix< T > &lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	delete_row (Matrix< T > &&lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	erase_component (const Matrix< T > &lhs, size_t i, size_t j)
template<ComponentType T>
constexpr Matrix< T >	erase_component (Matrix< T > &&lhs, size_t i, size_t j)
template<ComponentType T>
constexpr Matrix< T >	unerase_component (const Matrix< T > &lhs, size_t i, size_t j)
template<ComponentType T>
constexpr Matrix< T >	unerase_component (Matrix< T > &&lhs, size_t i, size_t j)
template<ComponentType T>
constexpr Matrix< T >	erase_columns (const Matrix< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	erase_columns (Matrix< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	erase_column (const Matrix< T > &lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	erase_column (Matrix< T > &&lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	unerase_columns (const Matrix< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	unerase_columns (Matrix< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	unerase_column (const Matrix< T > &lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	unerase_column (Matrix< T > &&lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	erase_rows (const Matrix< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	erase_rows (Matrix< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	erase_row (const Matrix< T > &lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	erase_row (Matrix< T > &&lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	unerase_rows (const Matrix< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	unerase_rows (Matrix< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	unerase_row (const Matrix< T > &lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	unerase_row (Matrix< T > &&lhs, size_t i)
template<ComponentType T>
Matrix< T >	reverse_rows (const Matrix< T > &M)
template<ComponentType T>
Matrix< T >	reverse_rows (Matrix< T > &&M)
template<ComponentType T>
Matrix< T >	reverse_columns (const Matrix< T > &M)
template<ComponentType T>
Matrix< T >	reverse_columns (Matrix< T > &&M)
template<ComponentType T>
constexpr Matrix< T >	fill (const Matrix< T > &m, const T &value)
template<ComponentType T>
constexpr Matrix< T >	fill (Matrix< T > &&m, const T &value)
template<ComponentType T>
constexpr Matrix< T >	transpose (const Matrix< T > &M)
template<ComponentType T>
constexpr Matrix< T >	transpose (Matrix< T > &&M)
template<FieldType T>
Matrix< T >	rref (const Matrix< T > &M)
template<FieldType T>
Matrix< T >	rref (Matrix< T > &&M)
template<FieldType T>
Matrix< T >	inverse (const Matrix< T > &M)
template<FieldType T>
Matrix< T >	inverse (Matrix< T > &&M)
template<ReliablyComparableType T>
constexpr bool	operator== (const Matrix< T > &lhs, const Matrix< T > &rhs)
	Equality of two matrices.
template<ReliablyComparableType T>
constexpr bool	operator!= (const Matrix< T > &lhs, const Matrix< T > &rhs)
	Negation of operator==.
template<ComponentType T>
Matrix< T >	PermutationMatrix (const std::vector< size_t > &perm)
	Permutation matrix P with P_{i, perm[i]} = 1.
template<ComponentType T>
constexpr Matrix< T >	ExchangeMatrix (size_t m)
	m × m exchange matrix (ones on the anti-diagonal)
template<ComponentType T>
constexpr Matrix< T >	HankelMatrix (const Vector< T > &v, size_t m, size_t n)
	m × n Hankel matrix from its anti-diagonal entries
template<ComponentType T>
constexpr Matrix< T >	UpperShiftMatrix (size_t m)
	m × m upper shift matrix (ones on the superdiagonal)
template<ComponentType T>
constexpr Matrix< T >	LowerShiftMatrix (size_t m)
	m × m lower shift matrix (ones on the subdiagonal); transpose of UpperShiftMatrix
template<CoefficientType T>
constexpr Matrix< T >	CompanionMatrix (const Polynomial< T > &poly)
	Companion matrix of a monic polynomial p(x) = x^n + a_{n−1} x^{n−1} + … + a_0.
template<CoefficientType T>
std::ostream &	operator<< (std::ostream &os, const Polynomial< T > &rhs)
template<CoefficientType T>
const Polynomial< T > &	ZeroPolynomial ()
	Constant polynomial 0 (cached).
template<CoefficientType T>
constexpr Polynomial< T >	operator+ (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator+ (Polynomial< T > &&lhs, const Polynomial< T > &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator+ (const Polynomial< T > &lhs, Polynomial< T > &&rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator+ (Polynomial< T > &&lhs, Polynomial< T > &&rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator- (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator- (Polynomial< T > &&lhs, const Polynomial< T > &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator- (const Polynomial< T > &lhs, Polynomial< T > &&rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator- (Polynomial< T > &&lhs, Polynomial< T > &&rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator* (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator* (Polynomial< T > &&lhs, const Polynomial< T > &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator* (const Polynomial< T > &lhs, Polynomial< T > &&rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator* (Polynomial< T > &&lhs, Polynomial< T > &&rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator/ (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator/ (Polynomial< T > &&lhs, const Polynomial< T > &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator% (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator% (Polynomial< T > &&lhs, const Polynomial< T > &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator* (const Polynomial< T > &lhs, const T &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator* (Polynomial< T > &&lhs, const T &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator* (const T &lhs, const Polynomial< T > &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator* (const T &lhs, Polynomial< T > &&rhs)
template<FieldType T>
constexpr Polynomial< T >	operator/ (const Polynomial< T > &lhs, const T &rhs)
template<FieldType T>
constexpr Polynomial< T >	operator/ (Polynomial< T > &&lhs, const T &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator* (const Polynomial< T > &lhs, size_t n)
template<CoefficientType T>
constexpr Polynomial< T >	operator* (Polynomial< T > &&lhs, size_t n)
template<CoefficientType T>
constexpr Polynomial< T >	operator* (size_t n, const Polynomial< T > &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	operator* (size_t n, Polynomial< T > &&rhs)
template<CoefficientType T>
std::pair< Polynomial< T >, Polynomial< T > >	poly_long_div (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<CoefficientType T>
std::pair< Polynomial< T >, Polynomial< T > >	poly_long_div (Polynomial< T > &&lhs, const Polynomial< T > &rhs)
template<CoefficientType T> requires FieldType<T>
constexpr Polynomial< T >	derivative (const Polynomial< T > &poly, size_t s)
template<CoefficientType T> requires FieldType<T>
constexpr Polynomial< T >	derivative (Polynomial< T > &&poly, size_t s)
template<CoefficientType T> requires FieldType<T>
constexpr Polynomial< T >	Hasse_derivative (const Polynomial< T > &poly, size_t s)
template<CoefficientType T> requires FieldType<T>
constexpr Polynomial< T >	Hasse_derivative (Polynomial< T > &&poly, size_t s)
template<CoefficientType T>
constexpr Polynomial< T >	reciprocal (const Polynomial< T > &poly)
template<CoefficientType T>
constexpr Polynomial< T >	reciprocal (Polynomial< T > &&poly)
template<CoefficientType T> requires ReliablyComparableType<T>
constexpr Polynomial< T >	shift_up (const Polynomial< T > &poly, size_t s)
template<CoefficientType T> requires ReliablyComparableType<T>
constexpr Polynomial< T >	shift_up (Polynomial< T > &&poly, size_t s)
template<CoefficientType T>
constexpr Polynomial< T >	shift_down (const Polynomial< T > &poly, size_t s)
template<CoefficientType T>
constexpr Polynomial< T >	shift_down (Polynomial< T > &&poly, size_t s)
template<CoefficientType T> requires FieldType<T>
constexpr Polynomial< T >	normalize (const Polynomial< T > &poly)
template<CoefficientType T> requires FieldType<T>
constexpr Polynomial< T >	normalize (Polynomial< T > &&poly)
template<ReliablyComparableType T>
constexpr bool	operator== (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<ReliablyComparableType T>
constexpr bool	operator!= (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<CoefficientType T>
constexpr Polynomial< T >	Monomial (size_t i, const T &a=T(1))
	Monomial a · xⁱ
template<CoefficientType T>
const Polynomial< T > &	OnePolynomial ()
	Constant polynomial 1 (cached).
template<CoefficientType T> requires FieldType<T>
Polynomial< T >	GCD (Polynomial< T > a, Polynomial< T > b, Polynomial< T > *s_ptr=nullptr, Polynomial< T > *t_ptr=nullptr)
	Greatest common divisor of two polynomials via the (extended) Euclidean algorithm.
template<CoefficientType T> requires FieldType<T>
Polynomial< T >	GCD (const std::vector< Polynomial< T > > &polys)
	Greatest common divisor of a list of polynomials, computed iteratively.
template<CoefficientType T> requires FieldType<T>
Polynomial< T >	LCM (const Polynomial< T > &a, const Polynomial< T > &b)
	Least common multiple lcm(a, b) = (a · b) / gcd(a, b).
template<CoefficientType T> requires FieldType<T>
Polynomial< T >	LCM (const std::vector< Polynomial< T > > &polys)
	Least common multiple of a list of polynomials, computed iteratively.
template<CoefficientType T>
constexpr Polynomial< T >	operator^ (const Polynomial< T > &base, int exponent)
	Polynomial exponentiation by square-and-multiply.
template<uint16_t p, size_t m>
constexpr Vector< Fp< p > >	ConwayCoefficients ()
	Coefficient vector [a₀, a₁, …, aₘ] of the Conway polynomial for 𝔽_{p^m}.
template<uint16_t p, size_t m>
constexpr Polynomial< Fp< p > >	ConwayPolynomial ()
	Conway polynomial for 𝔽_{p^m} as a Polynomial<Fp<p>>.
template<FiniteFieldType T>
Polynomial< T >	find_irreducible (size_t degree)
	Sample a random monic irreducible polynomial of degree degree over T.
template<ComponentType T>
T	inner_product (const Vector< T > &lhs, const Vector< T > &rhs)
	Inner product ⟨lhs, rhs⟩ = Σᵢ lhs[i] · rhs[i].
template<ComponentType T>
Vector< T >	Schur_product (const Vector< T > &lhs, const Vector< T > &rhs)
	Schur (component-wise) product.
template<ComponentType T>
Vector< T >	unit_vector (size_t length, size_t i)
	Length-length vector with T(1) at index i and zeros elsewhere.
template<ComponentType T>
std::ostream &	operator<< (std::ostream &os, const Vector< T > &rhs)
	Stream output as ( c₀, c₁, …, cₙ₋₁ ).
template<CoefficientType T>
	Vector (const Polynomial< T > &) -> Vector< T >
	Deduction guide: a vector constructed from a polynomial deduces the coefficient type.
template<ComponentType T>
Vector< T >	delete_component (const Vector< T > &lhs, size_t i)
template<ComponentType T>
Vector< T >	delete_component (Vector< T > &&lhs, size_t i)
template<ComponentType T>
constexpr Vector< T >	operator+ (const Vector< T > &lhs, const Vector< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	operator+ (Vector< T > &&lhs, const Vector< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	operator+ (const Vector< T > &lhs, Vector< T > &&rhs)
template<ComponentType T>
constexpr Vector< T >	operator+ (Vector< T > &&lhs, Vector< T > &&rhs)
template<ComponentType T>
constexpr Vector< T >	operator- (const Vector< T > &lhs, const Vector< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	operator- (Vector< T > &&lhs, const Vector< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	operator- (const Vector< T > &lhs, Vector< T > &&rhs)
template<ComponentType T>
constexpr Vector< T >	operator- (Vector< T > &&lhs, Vector< T > &&rhs)
template<ComponentType T>
constexpr Vector< T >	operator* (const Vector< T > &lhs, const T &rhs)
template<ComponentType T>
constexpr Vector< T >	operator* (Vector< T > &&lhs, const T &rhs)
template<ComponentType T>
constexpr Vector< T >	operator* (const T &lhs, const Vector< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	operator* (const T &lhs, Vector< T > &&rhs)
template<CoefficientType T>
constexpr Vector< T >	operator/ (const Vector< T > &lhs, const T &rhs)
template<CoefficientType T>
constexpr Vector< T >	operator/ (Vector< T > &&lhs, const T &rhs)
template<CoefficientType T>
Vector< T >	convolve (const Vector< T > &v, const Vector< T > &w)
	Discrete linear convolution (= coefficients of Polynomial(v) * Polynomial(w)); the result always has length v.get_n() + w.get_n() - 1.
template<CoefficientType T>
Vector< T >	randomize (const Vector< T > &v)
template<CoefficientType T>
Vector< T >	randomize (Vector< T > &&v)
template<ComponentType T>
Vector< T >	set_component (const Vector< T > &v, size_t i, const T &c)
template<ComponentType T>
Vector< T >	set_component (Vector< T > &&v, size_t i, const T &c)
template<ComponentType T>
constexpr Vector< T >	get_subvector (const Vector< T > &v, size_t start, size_t end)
template<ComponentType T>
constexpr Vector< T >	get_subvector (Vector< T > &&v, size_t start, size_t end)
template<ComponentType T>
constexpr Vector< T >	set_subvector (Vector< T > v, size_t start, const Vector< T > &w)
template<ComponentType T>
constexpr Vector< T >	set_subvector (Vector< T > &&v, size_t start, const Vector< T > &w)
template<ComponentType T>
constexpr Vector< T >	concatenate (const Vector< T > &lhs, const Vector< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	concatenate (Vector< T > &&lhs, const Vector< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	concatenate (const Vector< T > &lhs, Vector< T > &&rhs)
template<ComponentType T>
constexpr Vector< T >	concatenate (Vector< T > &&lhs, Vector< T > &&rhs)
template<ComponentType T>
Vector< T >	delete_components (const Vector< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
Vector< T >	delete_components (Vector< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
Vector< T >	erase_components (const Vector< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
Vector< T >	erase_components (Vector< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
Vector< T >	erase_component (const Vector< T > &lhs, size_t i)
template<ComponentType T>
Vector< T >	erase_component (Vector< T > &&lhs, size_t i)
template<ComponentType T>
Vector< T >	unerase_components (const Vector< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
Vector< T >	unerase_components (Vector< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
Vector< T >	unerase_component (const Vector< T > &lhs, size_t i)
template<ComponentType T>
Vector< T >	unerase_component (Vector< T > &&lhs, size_t i)
template<ComponentType T>
constexpr Vector< T >	pad_front (const Vector< T > &v, size_t n)
template<ComponentType T>
constexpr Vector< T >	pad_front (Vector< T > &&v, size_t n)
template<ComponentType T>
constexpr Vector< T >	pad_back (const Vector< T > &v, size_t n)
template<ComponentType T>
constexpr Vector< T >	pad_back (Vector< T > &&v, size_t n)
template<ComponentType T>
constexpr Vector< T >	rotate_left (const Vector< T > &v, size_t i)
template<ComponentType T>
constexpr Vector< T >	rotate_left (Vector< T > &&v, size_t i)
template<ComponentType T>
constexpr Vector< T >	rotate_right (const Vector< T > &v, size_t i)
template<ComponentType T>
constexpr Vector< T >	rotate_right (Vector< T > &&v, size_t i)
template<ComponentType T>
constexpr Vector< T >	reverse (const Vector< T > &v)
template<ComponentType T>
constexpr Vector< T >	reverse (Vector< T > &&v)
template<ComponentType T>
constexpr Vector< T >	fill (const Vector< T > &v, const T &value)
template<ComponentType T>
constexpr Vector< T >	fill (Vector< T > &&v, const T &value)
template<ReliablyComparableType T>
constexpr bool	operator== (const Vector< T > &lhs, const Vector< T > &rhs)
template<ReliablyComparableType T>
constexpr bool	operator!= (const Vector< T > &lhs, const Vector< T > &rhs)
Field Arithmetic Operators
Free CRTP operators (+, −, *, /, ^) for any CECCO::FieldType Each operator constructs a result by calling T's compound assignment, with rvalue overloads that move from a temporary instead of copying. Scalar multiplication takes the integer on either side. Division throws std::invalid_argument if the right operand is zero. operator^ exponentiates by square-and-multiply via CECCO::sqm. Warning operator^ does not follow C++ precedence for ^: in b * a ^ p the parser evaluates (b * a) ^ p. Parenthesise as b * (a ^ p), or call CECCO::sqm directly.
template<FieldType T>
constexpr T	operator+ (const T &lhs, const T &rhs)
template<FieldType T>
constexpr T	operator+ (T &&lhs, const T &rhs)
template<FieldType T>
constexpr T	operator+ (const T &lhs, T &&rhs)
template<FieldType T>
constexpr T	operator+ (T &&lhs, T &&rhs)
template<FieldType T>
constexpr T	operator- (const T &lhs, const T &rhs)
template<FieldType T>
constexpr T	operator- (T &&lhs, const T &rhs)
template<FieldType T>
constexpr T	operator- (const T &lhs, T &&rhs)
template<FieldType T>
constexpr T	operator- (T &&lhs, T &&rhs)
template<FieldType T>
constexpr T	operator* (const T &lhs, const T &rhs)
template<FieldType T>
constexpr T	operator* (T &&lhs, const T &rhs)
template<FieldType T>
constexpr T	operator* (const T &lhs, T &&rhs)
template<FieldType T>
constexpr T	operator* (T &&lhs, T &&rhs)
template<FieldType T>
constexpr T	operator* (const T &lhs, int rhs)
template<FieldType T>
constexpr T	operator* (int lhs, const T &rhs)
template<FieldType T>
constexpr T	operator* (T &&lhs, int rhs)
template<FieldType T>
constexpr T	operator* (int lhs, T &&rhs)
template<FieldType T>
T	operator/ (const T &lhs, const T &rhs)
template<FieldType T>
T	operator/ (T &&lhs, const T &rhs)
template<FieldType T>
constexpr T	operator^ (const T &base, int exponent)
template<FieldType T>
constexpr T	operator^ (T &&base, int exponent)
Error control coding-related functions
double	dE (const Vector< std::complex< double > > &lhs, const Vector< std::complex< double > > &rhs)
	Euclidean distance ‖lhs − rhs‖₂ = √(Σᵢ |lhs[i] − rhs[i]|²) for complex vectors.
template<ReliablyComparableType T>
constexpr size_t	wH (const Vector< T > &v)
	Hamming weight; see Vector::wH for semantics.
template<ReliablyComparableType T>
std::vector< size_t >	supp (const Vector< T > &v)
	Support; see Vector::supp for semantics.
template<ReliablyComparableType T>
size_t	dH (const Vector< T > &lhs, const Vector< T > &rhs)
	Hamming distance dₕ(lhs, rhs) = wₕ(lhs − rhs).
template<ReliablyComparableType T>
size_t	dH (Vector< T > &&lhs, const Vector< T > &rhs)
template<ReliablyComparableType T>
size_t	dH (const Vector< T > &lhs, Vector< T > &&rhs)
template<ReliablyComparableType T>
size_t	dH (Vector< T > &&lhs, Vector< T > &&rhs)
template<ReliablyComparableType T>
constexpr size_t	burst_length (const Vector< T > &v)
	Burst length; see Vector::burst_length for semantics.
template<ReliablyComparableType T>
constexpr size_t	cyclic_burst_length (const Vector< T > &v)
	Cyclic burst length; see Vector::cyclic_burst_length for semantics.

Variables
constexpr std::string_view	ERASURE_MARKER = "X"

Detailed Description

Provides a framework for error correcting codes.

Typedef Documentation

base_t

template<class B>

using CECCO::base_t = std::remove_cvref_t<B>

Definition at line 6975 of file codes.hpp.

BSC

using CECCO::BSC = SDMC<Fp<2>>

Binary Symmetric Channel: type alias for SDMC<Fp<2>>.

Bits are flipped with probability pe.

See also

CECCO::SDMC, CECCO::BEC

Definition at line 366 of file blocks.hpp.

field_t

template<class C>

using CECCO::field_t = typename base_t<C>::FIELD

Definition at line 6978 of file codes.hpp.

label_t

template<uint16_t p, uint8_t m = 1>

using CECCO::label_t = typename std::conditional_t<sqm(p, m) < 255, uint8_t, uint16_t>

Definition at line 779 of file fields.hpp.

Enumeration Type Documentation

list_method_t

enum class CECCO::list_method_t

strong

Enumerator
Viterbi
Viterbi_soft
SA
SA_optimized
GSA
GSA_optimized
KVA

Definition at line 451 of file codes.hpp.

list_processing_t

enum class CECCO::list_processing_t

strong

Enumerator
pick_first
pick_random

Definition at line 453 of file codes.hpp.

LutMode

enum class CECCO::LutMode

strong

LUT generation mode for field operations.

Enumerator
CompileTime	Generate LUTs at compile-time using constexpr (default).
RunTime	Generate LUTs at runtime using lazy initialization.

Definition at line 55 of file field_concepts_traits.hpp.

method_t

enum class CECCO::method_t

strong

Enumerator
BD
standard_array
BD_standard_array
boosted_BD_standard_array
ML
ML_soft
Viterbi
Viterbi_soft
BCJR
ssMAP
BP
recursive
Meggitt
WBA
WBA_optimized
BMA
OSD
LC_OSD
WBA_EE
BMA_EE
BD_EE
ML_EE
Viterbi_EE
recursive_EE
GMD

Definition at line 421 of file codes.hpp.

termination_t

enum class CECCO::termination_t

strong

Enumerator
zero_terminated
tailbitten

Definition at line 5387 of file codes.hpp.

Function Documentation

add_column() [1/2]

template<ComponentType T>

Matrix< T > CECCO::add_column	(	const Matrix< T > &	M,
		size_t	i,
		size_t	j )

Definition at line 3390 of file matrices.hpp.

add_column() [2/2]

template<ComponentType T>

Matrix< T > CECCO::add_column	(	Matrix< T > &&	M,
		size_t	i,
		size_t	j )

Definition at line 3404 of file matrices.hpp.

add_row() [1/2]

template<ComponentType T>

Matrix< T > CECCO::add_row	(	const Matrix< T > &	M,
		size_t	i,
		size_t	j )

Definition at line 3383 of file matrices.hpp.

add_row() [2/2]

template<ComponentType T>

Matrix< T > CECCO::add_row	(	Matrix< T > &&	M,
		size_t	i,
		size_t	j )

Definition at line 3397 of file matrices.hpp.

add_scaled_column() [1/2]

template<ComponentType T>

Matrix< T > CECCO::add_scaled_column	(	const Matrix< T > &	M,
		const T &	s,
		size_t	i,
		size_t	j )

Definition at line 3362 of file matrices.hpp.

add_scaled_column() [2/2]

template<ComponentType T>

Matrix< T > CECCO::add_scaled_column	(	Matrix< T > &&	M,
		const T &	s,
		size_t	i,
		size_t	j )

Definition at line 3376 of file matrices.hpp.

add_scaled_row() [1/2]

template<ComponentType T>

Matrix< T > CECCO::add_scaled_row	(	const Matrix< T > &	M,
		const T &	s,
		size_t	i,
		size_t	j )

Definition at line 3355 of file matrices.hpp.

add_scaled_row() [2/2]

template<ComponentType T>

Matrix< T > CECCO::add_scaled_row	(	Matrix< T > &&	M,
		const T &	s,
		size_t	i,
		size_t	j )

Definition at line 3369 of file matrices.hpp.

augment()

template<class B>

auto CECCO::augment	(	B &&	base,
		size_t	j,
		const Vector< field_t< B > > &	w )

Definition at line 7002 of file codes.hpp.

bin() [1/2]

template<>

InfInt CECCO::bin ( const InfInt & n, InfInt k )

inline

Binomial coefficient specialization for InfInt.

Parameters

n	Total number of items
k	Number of items to choose

Returns

C(n,k) as an InfInt

Builds numerator and denominator separately, then performs one division.

Definition at line 281 of file helpers.hpp.

Here is the call graph for this function:

bin() [2/2]

template<class T>

T CECCO::bin	(	const T &	n,
		T	k )

Binomial coefficient C(n,k).

Template Parameters

T	Integer type

Parameters

n	Total number of items
k	Number of items to choose

Returns

C(n,k) = n! / (k! * (n-k)!)

Uses the multiplicative formula and the symmetry C(n,k) = C(n,n-k).

Definition at line 263 of file helpers.hpp.

burst_length()

template<ReliablyComparableType T>

size_t CECCO::burst_length ( const Vector< T > & v )

constexpr

Burst length; see Vector::burst_length for semantics.

Definition at line 1713 of file vectors.hpp.

BurstUpperBound()

template<FiniteFieldType T>

size_t CECCO::BurstUpperBound	(	size_t	n,
		size_t	ell )

Definition at line 216 of file code_bounds.hpp.

CompanionMatrix()

template<CoefficientType T>

Matrix< T > CECCO::CompanionMatrix ( const Polynomial< T > & poly )

constexpr

Companion matrix of a monic polynomial p(x) = x^n + a_{n−1} x^{n−1} + … + a_0.

Parameters

poly	Monic polynomial of degree n

Returns

n × n matrix whose characteristic polynomial is poly

Built from a lower shift matrix; the last column holds the negated coefficients of poly.

Exceptions

std::invalid_argument

if poly is not monic

Definition at line 4050 of file matrices.hpp.

concatenate() [1/4]

template<ComponentType T>

Vector< T > CECCO::concatenate ( const Vector< T > & lhs, const Vector< T > & rhs )

constexpr

Definition at line 1397 of file vectors.hpp.

concatenate() [2/4]

template<ComponentType T>

Vector< T > CECCO::concatenate ( const Vector< T > & lhs, Vector< T > && rhs )

constexpr

Definition at line 1411 of file vectors.hpp.

concatenate() [3/4]

template<ComponentType T>

Vector< T > CECCO::concatenate ( Vector< T > && lhs, const Vector< T > & rhs )

constexpr

Definition at line 1404 of file vectors.hpp.

concatenate() [4/4]

template<ComponentType T>

Vector< T > CECCO::concatenate ( Vector< T > && lhs, Vector< T > && rhs )

constexpr

Definition at line 1418 of file vectors.hpp.

convolve()

template<CoefficientType T>

Vector< T > CECCO::convolve	(	const Vector< T > &	v,
		const Vector< T > &	w )

Discrete linear convolution (= coefficients of Polynomial(v) * Polynomial(w)); the result always has length v.get_n() + w.get_n() - 1.

Exceptions

std::invalid_argument

if either input is empty

Definition at line 1341 of file vectors.hpp.

ConwayCoefficients()

template<uint16_t p, size_t m>

Vector< Fp< p > > CECCO::ConwayCoefficients ( )

constexpr

Coefficient vector [a₀, a₁, …, aₘ] of the Conway polynomial for 𝔽_{p^m}.

Template Parameters

p	Prime characteristic
m	Extension degree

Returns

Coefficients low-to-high; empty vector if the (p, m) pair is not in the built-in table

The built-in table covers all primes ≤ 97 and degrees ≤ ~13 (more for small p).

Definition at line 1517 of file polynomials.hpp.

ConwayPolynomial()

template<uint16_t p, size_t m>

Polynomial< Fp< p > > CECCO::ConwayPolynomial ( )

constexpr

Conway polynomial for 𝔽_{p^m} as a Polynomial<Fp<p>>.

Wraps ConwayCoefficients.

Exceptions

std::logic_error

if (p, m) is not tabulated

Definition at line 1710 of file polynomials.hpp.

cyclic_burst_length()

template<ReliablyComparableType T>

size_t CECCO::cyclic_burst_length ( const Vector< T > & v )

constexpr

Cyclic burst length; see Vector::cyclic_burst_length for semantics.

Definition at line 1719 of file vectors.hpp.

daa()

template<class T>

T CECCO::daa ( T b, int m )

constexpr

Scalar multiplication by double-and-add.

Template Parameters

T	Type supporting addition and unary minus

Parameters

b	Multiplicand
m	Integer multiplier

Returns

b * m

For negative multipliers, computes (-b) * |m|.

Note

Returns T(0) for m = 0.

Definition at line 435 of file helpers.hpp.

dE()

double CECCO::dE ( const Vector< std::complex< double > > & lhs, const Vector< std::complex< double > > & rhs )

inline

Euclidean distance ‖lhs − rhs‖₂ = √(Σᵢ |lhs[i] − rhs[i]|²) for complex vectors.

Exceptions

std::invalid_argument

if lengths differ

Definition at line 1727 of file vectors.hpp.

delete_column() [1/2]

template<ComponentType T>

Matrix< T > CECCO::delete_column ( const Matrix< T > & lhs, size_t i )

constexpr

Definition at line 3425 of file matrices.hpp.

delete_column() [2/2]

template<ComponentType T>

Matrix< T > CECCO::delete_column ( Matrix< T > && lhs, size_t i )

constexpr

Definition at line 3432 of file matrices.hpp.

delete_columns() [1/2]

template<ComponentType T>

Matrix< T > CECCO::delete_columns ( const Matrix< T > & lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3411 of file matrices.hpp.

delete_columns() [2/2]

template<ComponentType T>

Matrix< T > CECCO::delete_columns ( Matrix< T > && lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3418 of file matrices.hpp.

delete_component() [1/2]

template<ComponentType T>

Vector< T > CECCO::delete_component	(	const Vector< T > &	lhs,
		size_t	i )

Definition at line 840 of file vectors.hpp.

delete_component() [2/2]

template<ComponentType T>

Vector< T > CECCO::delete_component	(	Vector< T > &&	lhs,
		size_t	i )

Definition at line 847 of file vectors.hpp.

delete_components() [1/2]

template<ComponentType T>

Vector< T > CECCO::delete_components	(	const Vector< T > &	lhs,
		const std::vector< size_t > &	v )

Definition at line 1425 of file vectors.hpp.

delete_components() [2/2]

template<ComponentType T>

Vector< T > CECCO::delete_components	(	Vector< T > &&	lhs,
		const std::vector< size_t > &	v )

Definition at line 1432 of file vectors.hpp.

delete_row() [1/2]

template<ComponentType T>

Matrix< T > CECCO::delete_row ( const Matrix< T > & lhs, size_t i )

constexpr

Definition at line 3453 of file matrices.hpp.

delete_row() [2/2]

template<ComponentType T>

Matrix< T > CECCO::delete_row ( Matrix< T > && lhs, size_t i )

constexpr

Definition at line 3460 of file matrices.hpp.

delete_rows() [1/2]

template<ComponentType T>

Matrix< T > CECCO::delete_rows ( const Matrix< T > & lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3439 of file matrices.hpp.

delete_rows() [2/2]

template<ComponentType T>

Matrix< T > CECCO::delete_rows ( Matrix< T > && lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3446 of file matrices.hpp.

derivative() [1/2]

template<CoefficientType T>
requires FieldType<T>

Polynomial< T > CECCO::derivative ( const Polynomial< T > & poly, size_t s )

constexpr

Definition at line 1214 of file polynomials.hpp.

derivative() [2/2]

template<CoefficientType T>
requires FieldType<T>

Polynomial< T > CECCO::derivative ( Polynomial< T > && poly, size_t s )

constexpr

Definition at line 1223 of file polynomials.hpp.

dH() [1/8]

template<ReliablyComparableType T>

size_t CECCO::dH	(	const Matrix< T > &	lhs,
		const Matrix< T > &	rhs )

Hamming distance dₕ(lhs, rhs) = wₕ(lhs − rhs).

Number of matrix components in which lhs and rhs differ. Under CECCO_ERASURE_SUPPORT, positions where either side is erased are not counted.

Exceptions

std::invalid_argument

if dimensions differ

Definition at line 3145 of file matrices.hpp.

dH() [2/8]

template<ReliablyComparableType T>

size_t CECCO::dH	(	const Matrix< T > &	lhs,
		Matrix< T > &&	rhs )

Definition at line 3164 of file matrices.hpp.

dH() [3/8]

template<ReliablyComparableType T>

size_t CECCO::dH	(	const Vector< T > &	lhs,
		const Vector< T > &	rhs )

Hamming distance dₕ(lhs, rhs) = wₕ(lhs − rhs).

Number of positions in which lhs and rhs differ. Under CECCO_ERASURE_SUPPORT, positions where either side is erased are not counted (subtraction propagates the erasure marker, and wH skips erased components).

Exceptions

std::invalid_argument

if lengths differ

Definition at line 1676 of file vectors.hpp.

dH() [4/8]

template<ReliablyComparableType T>

size_t CECCO::dH	(	const Vector< T > &	lhs,
		Vector< T > &&	rhs )

Definition at line 1695 of file vectors.hpp.

dH() [5/8]

template<ReliablyComparableType T>

size_t CECCO::dH	(	Matrix< T > &&	lhs,
		const Matrix< T > &	rhs )

Definition at line 3155 of file matrices.hpp.

dH() [6/8]

template<ReliablyComparableType T>

size_t CECCO::dH	(	Matrix< T > &&	lhs,
		Matrix< T > &&	rhs )

Definition at line 3173 of file matrices.hpp.

dH() [7/8]

template<ReliablyComparableType T>

size_t CECCO::dH	(	Vector< T > &&	lhs,
		const Vector< T > &	rhs )

Definition at line 1686 of file vectors.hpp.

dH() [8/8]

template<ReliablyComparableType T>

size_t CECCO::dH	(	Vector< T > &&	lhs,
		Vector< T > &&	rhs )

Definition at line 1703 of file vectors.hpp.

diagonal_join() [1/3]

template<ComponentType T>

Matrix< T > CECCO::diagonal_join	(	const Matrix< T > &	lhs,
		const Matrix< T > &	rhs )

Definition at line 3257 of file matrices.hpp.

diagonal_join() [2/3]

template<ComponentType T>

Matrix< T > CECCO::diagonal_join	(	Matrix< T > &&	lhs,
		const Matrix< T > &	rhs )

Definition at line 3264 of file matrices.hpp.

diagonal_join() [3/3]

template<ComponentType T>

Matrix< T > CECCO::diagonal_join	(	Matrix< T > &&	lhs,
		Matrix< T > &&	rhs )

Definition at line 3271 of file matrices.hpp.

DiagonalMatrix()

template<ComponentType T>

Matrix< T > CECCO::DiagonalMatrix ( const Vector< T > & v )

constexpr

Diagonal matrix with diagonal v (strongest tag of details::Zero, details::Identity, details::Diagonal).

Parameters

v	Vector of diagonal entries; the result is v.length() × v.length()

Returns

Diagonal matrix with v[i] on position (i, i), zeros elsewhere

Definition at line 3895 of file matrices.hpp.

dual()

template<FieldType T>

auto CECCO::dual

(

const LinearCode< T > &

C

)

Definition at line 6957 of file codes.hpp.

EliasUpperBound()

template<FiniteFieldType T>

long double CECCO::EliasUpperBound	(	size_t	n,
		size_t	dmin )

Definition at line 120 of file code_bounds.hpp.

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equivalent()

template<FieldType L, FieldType R>

bool CECCO::equivalent	(	const LinearCode< L > &	lhs,
		const LinearCode< R > &	rhs )

Definition at line 7116 of file codes.hpp.

erase_column() [1/2]

template<ComponentType T>

Matrix< T > CECCO::erase_column ( const Matrix< T > & lhs, size_t i )

constexpr

Definition at line 3511 of file matrices.hpp.

erase_column() [2/2]

template<ComponentType T>

Matrix< T > CECCO::erase_column ( Matrix< T > && lhs, size_t i )

constexpr

Definition at line 3518 of file matrices.hpp.

erase_columns() [1/2]

template<ComponentType T>

Matrix< T > CECCO::erase_columns ( const Matrix< T > & lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3497 of file matrices.hpp.

erase_columns() [2/2]

template<ComponentType T>

Matrix< T > CECCO::erase_columns ( Matrix< T > && lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3504 of file matrices.hpp.

erase_component() [1/4]

template<ComponentType T>

Matrix< T > CECCO::erase_component ( const Matrix< T > & lhs, size_t i, size_t j )

constexpr

Definition at line 3469 of file matrices.hpp.

erase_component() [2/4]

template<ComponentType T>

Vector< T > CECCO::erase_component	(	const Vector< T > &	lhs,
		size_t	i )

Definition at line 1455 of file vectors.hpp.

erase_component() [3/4]

template<ComponentType T>

Matrix< T > CECCO::erase_component ( Matrix< T > && lhs, size_t i, size_t j )

constexpr

Definition at line 3476 of file matrices.hpp.

erase_component() [4/4]

template<ComponentType T>

Vector< T > CECCO::erase_component	(	Vector< T > &&	lhs,
		size_t	i )

Definition at line 1462 of file vectors.hpp.

erase_components() [1/2]

template<ComponentType T>

Vector< T > CECCO::erase_components	(	const Vector< T > &	lhs,
		const std::vector< size_t > &	v )

Definition at line 1441 of file vectors.hpp.

erase_components() [2/2]

template<ComponentType T>

Vector< T > CECCO::erase_components	(	Vector< T > &&	lhs,
		const std::vector< size_t > &	v )

Definition at line 1448 of file vectors.hpp.

erase_row() [1/2]

template<ComponentType T>

Matrix< T > CECCO::erase_row ( const Matrix< T > & lhs, size_t i )

constexpr

Definition at line 3567 of file matrices.hpp.

erase_row() [2/2]

template<ComponentType T>

Matrix< T > CECCO::erase_row ( Matrix< T > && lhs, size_t i )

constexpr

Definition at line 3574 of file matrices.hpp.

erase_rows() [1/2]

template<ComponentType T>

Matrix< T > CECCO::erase_rows ( const Matrix< T > & lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3553 of file matrices.hpp.

erase_rows() [2/2]

template<ComponentType T>

Matrix< T > CECCO::erase_rows ( Matrix< T > && lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3560 of file matrices.hpp.

ExchangeMatrix()

template<ComponentType T>

Matrix< T > CECCO::ExchangeMatrix ( size_t m )

constexpr

m × m exchange matrix (ones on the anti-diagonal)

Parameters

m	Side length

Returns

Matrix with E_{i, j} = 1 iff i + j = m − 1

Definition at line 3881 of file matrices.hpp.

expurgate() [1/3]

template<class C>

auto CECCO::expurgate	(	C &&	code,
		size_t	j )

Definition at line 7091 of file codes.hpp.

expurgate() [2/3]

template<FieldType T>

EmptyCode< T > CECCO::expurgate	(	const EmptyCode< T > &	,
		const std::vector< size_t > &	)

Definition at line 7085 of file codes.hpp.

expurgate() [3/3]

template<FieldType T>

LinearCode< T > CECCO::expurgate	(	const LinearCode< T > &	C,
		const std::vector< size_t > &	v )

Definition at line 7071 of file codes.hpp.

extend() [1/2]

template<class B>

auto CECCO::extend

(

B &&

base

)

Definition at line 6988 of file codes.hpp.

extend() [2/2]

template<class B>

auto CECCO::extend	(	B &&	base,
		size_t	i,
		const Vector< field_t< B > > &	v )

Definition at line 6981 of file codes.hpp.

fac()

template<class T>

T CECCO::fac

(

T

a

)

Factorial a!

Template Parameters

T	Integer type

Parameters

a	Non-negative integer

Returns

a! = a * (a-1) * ... * 2 * 1

Definition at line 244 of file helpers.hpp.

fill() [1/4]

template<ComponentType T>

Matrix< T > CECCO::fill ( const Matrix< T > & m, const T & value )

constexpr

Definition at line 3639 of file matrices.hpp.

fill() [2/4]

template<ComponentType T>

Vector< T > CECCO::fill ( const Vector< T > & v, const T & value )

constexpr

Definition at line 1569 of file vectors.hpp.

fill() [3/4]

template<ComponentType T>

Matrix< T > CECCO::fill ( Matrix< T > && m, const T & value )

constexpr

Definition at line 3646 of file matrices.hpp.

fill() [4/4]

template<ComponentType T>

Vector< T > CECCO::fill ( Vector< T > && v, const T & value )

constexpr

Definition at line 1576 of file vectors.hpp.

find_irreducible()

template<FiniteFieldType T>

Polynomial< T > CECCO::find_irreducible

(

size_t

degree

)

Sample a random monic irreducible polynomial of degree degree over T.

Tries random polynomials until Polynomial::is_irreducible accepts one. Runtime is bounded in expectation by the density of irreducibles, but unbounded in the worst case; suitable as a modulus for CECCO::Ext.

Definition at line 1726 of file polynomials.hpp.

find_maxima()

template<class T>

std::vector< size_t > CECCO::find_maxima

(

const std::vector< T > &

v

)

Indices of all maximum elements.

Template Parameters

T	Element type (must support operator< for comparison)

Parameters

v	Input vector

Returns

Indices i with v[i] == max(v); empty if v is empty

Uses two passes over v.

Definition at line 148 of file helpers.hpp.

GCD() [1/3]

template<CoefficientType T>
requires FieldType<T>

Polynomial< T > CECCO::GCD

(

const std::vector< Polynomial< T > > &

polys

)

Greatest common divisor of a list of polynomials, computed iteratively.

Returns

gcd(p₁, p₂, …, pₙ)

Exceptions

std::invalid_argument

if polys is empty

Definition at line 1447 of file polynomials.hpp.

GCD() [2/3]

template<CoefficientType T>
requires FieldType<T>

Polynomial< T > CECCO::GCD	(	Polynomial< T >	a,
		Polynomial< T >	b,
		Polynomial< T > *	s_ptr = nullptr,
		Polynomial< T > *	t_ptr = nullptr )

Greatest common divisor of two polynomials via the (extended) Euclidean algorithm.

Parameters

a	First polynomial
b	Second polynomial
s_ptr	Optional out-pointer for the Bézout coefficient of a
t_ptr	Optional out-pointer for the Bézout coefficient of b

Returns

gcd(a, b); if both s_ptr and t_ptr are non-null, additionally gcd(a, b) = s·a + t·b

Operands are reordered internally so that the higher-degree one drives the recursion.

Definition at line 1407 of file polynomials.hpp.

GCD() [3/3]

template<class T>

T CECCO::GCD ( T a, T b, T * s = nullptr, T * t = nullptr )

constexpr

Greatest common divisor and optional Bézout coefficients.

Template Parameters

T	Signed integral type

Parameters

a	First integer
b	Second integer
s	Pointer to store Bézout coefficient for a (optional)
t	Pointer to store Bézout coefficient for b (optional)

Returns

Greatest common divisor of a and b

If s and t are non-null, stores coefficients satisfying a*s + b*t = gcd(a,b).

Definition at line 188 of file helpers.hpp.

gen()

std::mt19937 & CECCO::gen ( )

inline

Current thread's random number generator.

Returns

Reference to thread-local random number generator

Equivalent to RNG::get.

Definition at line 137 of file helpers.hpp.

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get_submatrix()

template<ComponentType T>

Matrix< T > CECCO::get_submatrix	(	const Matrix< T > &	M,
		size_t	i,
		size_t	j,
		size_t	h,
		size_t	w )

Definition at line 3196 of file matrices.hpp.

get_subvector() [1/2]

template<ComponentType T>

Vector< T > CECCO::get_subvector ( const Vector< T > & v, size_t start, size_t end )

constexpr

Definition at line 1377 of file vectors.hpp.

get_subvector() [2/2]

template<ComponentType T>

Vector< T > CECCO::get_subvector ( Vector< T > && v, size_t start, size_t end )

constexpr

Definition at line 1382 of file vectors.hpp.

GilbertVarshamovLowerBound()

template<FiniteFieldType T>

size_t CECCO::GilbertVarshamovLowerBound	(	size_t	n,
		size_t	dmin )

Definition at line 200 of file code_bounds.hpp.

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GriesmerUpperBound()

template<FiniteFieldType T>

size_t CECCO::GriesmerUpperBound	(	size_t	n,
		size_t	dmin )

Definition at line 151 of file code_bounds.hpp.

HammingUpperBound()

template<FiniteFieldType T>

long double CECCO::HammingUpperBound	(	size_t	n,
		size_t	dmin )

Definition at line 35 of file code_bounds.hpp.

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HankelMatrix()

template<ComponentType T>

Matrix< T > CECCO::HankelMatrix ( const Vector< T > & v, size_t m, size_t n )

constexpr

m × n Hankel matrix from its anti-diagonal entries

Parameters

v	Anti-diagonal values; length m + n − 1
m	Number of rows
n	Number of columns

Returns

Hankel matrix; each ascending anti-diagonal is constant

Constructed by reversing the columns of ToeplitzMatrix(reverse(v), m, n).

Exceptions

std::invalid_argument

if v.length() != m + n - 1

Definition at line 3973 of file matrices.hpp.

Hasse_derivative() [1/2]

template<CoefficientType T>
requires FieldType<T>

Polynomial< T > CECCO::Hasse_derivative ( const Polynomial< T > & poly, size_t s )

constexpr

Definition at line 1232 of file polynomials.hpp.

Hasse_derivative() [2/2]

template<CoefficientType T>
requires FieldType<T>

Polynomial< T > CECCO::Hasse_derivative ( Polynomial< T > && poly, size_t s )

constexpr

Definition at line 1241 of file polynomials.hpp.

horizontal_join() [1/3]

template<ComponentType T>

Matrix< T > CECCO::horizontal_join	(	const Matrix< T > &	lhs,
		const Matrix< T > &	rhs )

Definition at line 3215 of file matrices.hpp.

horizontal_join() [2/3]

template<ComponentType T>

Matrix< T > CECCO::horizontal_join	(	Matrix< T > &&	lhs,
		const Matrix< T > &	rhs )

Definition at line 3222 of file matrices.hpp.

horizontal_join() [3/3]

template<ComponentType T>

Matrix< T > CECCO::horizontal_join	(	Matrix< T > &&	lhs,
		Matrix< T > &&	rhs )

Definition at line 3229 of file matrices.hpp.

identical()

template<FieldType L, FieldType R>

bool CECCO::identical	(	const LinearCode< L > &	lhs,
		const LinearCode< R > &	rhs )

Definition at line 7111 of file codes.hpp.

IdentityMatrix()

template<ComponentType T>

Matrix< T > CECCO::IdentityMatrix ( size_t m )

constexpr

m × m identity matrix I_m

Parameters

m	Side length

Returns

Newly constructed identity matrix; for m = 0 the tag is details::Zero

Definition at line 3838 of file matrices.hpp.

inner_product()

template<ComponentType T>

T CECCO::inner_product	(	const Vector< T > &	lhs,
		const Vector< T > &	rhs )

Inner product ⟨lhs, rhs⟩ = Σᵢ lhs[i] · rhs[i].

For complex inputs this is the standard product (not the conjugate inner product).

Exceptions

std::invalid_argument

if lengths differ

Definition at line 1590 of file vectors.hpp.

inverse() [1/2]

template<FieldType T>

Matrix< T > CECCO::inverse

(

const Matrix< T > &

M

)

Definition at line 3681 of file matrices.hpp.

inverse() [2/2]

template<FieldType T>

Matrix< T > CECCO::inverse

(

Matrix< T > &&

M

)

Definition at line 3688 of file matrices.hpp.

is_prime()

template<class T>

bool CECCO::is_prime ( T a )

constexprnoexcept

Primality test by trial division.

Template Parameters

T	Unsigned integer type

Parameters

a	Number to test for primality

Returns

true if a is prime, false otherwise

Tests odd divisors up to √a. Returns false for a ≤ 1 and even a > 2.

Definition at line 167 of file helpers.hpp.

JohnsonUpperBound()

template<FiniteFieldType T>

long double CECCO::JohnsonUpperBound	(	size_t	n,
		size_t	dmin )

Definition at line 71 of file code_bounds.hpp.

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Kronecker_product() [1/3]

template<ComponentType T>

Matrix< T > CECCO::Kronecker_product	(	const Matrix< T > &	lhs,
		const Matrix< T > &	rhs )

Definition at line 3278 of file matrices.hpp.

Kronecker_product() [2/3]

template<ComponentType T>

Matrix< T > CECCO::Kronecker_product	(	Matrix< T > &&	lhs,
		const Matrix< T > &	rhs )

Definition at line 3285 of file matrices.hpp.

Kronecker_product() [3/3]

template<ComponentType T>

Matrix< T > CECCO::Kronecker_product	(	Matrix< T > &&	lhs,
		Matrix< T > &&	rhs )

Definition at line 3292 of file matrices.hpp.

LCM() [1/2]

template<CoefficientType T>
requires FieldType<T>

Polynomial< T > CECCO::LCM	(	const Polynomial< T > &	a,
		const Polynomial< T > &	b )

Least common multiple lcm(a, b) = (a · b) / gcd(a, b).

Definition at line 1463 of file polynomials.hpp.

LCM() [2/2]

template<CoefficientType T>
requires FieldType<T>

Polynomial< T > CECCO::LCM

(

const std::vector< Polynomial< T > > &

polys

)

Least common multiple of a list of polynomials, computed iteratively.

Returns

lcm(p₁, p₂, …, pₙ)

Exceptions

std::invalid_argument

if polys is empty

Definition at line 1476 of file polynomials.hpp.

lengthen() [1/2]

template<class B>

auto CECCO::lengthen	(	B &&	base,
		size_t	j,
		const Vector< field_t< B > > &	w )

Definition at line 7023 of file codes.hpp.

lengthen() [2/2]

template<class B>

auto CECCO::lengthen	(	B &&	base,
		size_t	j,
		const Vector< field_t< B > > &	w,
		size_t	i,
		const Vector< field_t< B > > &	v )

Definition at line 7016 of file codes.hpp.

LLRCalculator() [1/3]

CECCO::LLRCalculator

(

const BI_AWGN &

)

-> LLRCalculator< Fp< 2 > >

LLRCalculator() [2/3]

CECCO::LLRCalculator	(	const NRZMapper &	,
		const AWGN &	) -> LLRCalculator< Fp< 2 > >

LLRCalculator() [3/3]

template<FiniteFieldType T>

CECCO::LLRCalculator

(

const SDMEC< T > &

)

-> LLRCalculator< T >

log2()

long double CECCO::log2 ( const InfInt & v )

inline

Base-2 logarithm of a positive InfInt of arbitrary magnitude.

Parameters

v	Positive integer

Returns

log2(v) as long double

Exceptions

std::invalid_argument

if v <= 0

Evaluates the leading decimal digits and shifts by the remaining length, avoiding any conversion of v to a builtin integer type (which would overflow beyond 2^64).

Definition at line 304 of file helpers.hpp.

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LowerShiftMatrix()

template<ComponentType T>

Matrix< T > CECCO::LowerShiftMatrix ( size_t m )

constexpr

m × m lower shift matrix (ones on the subdiagonal); transpose of UpperShiftMatrix

Parameters

m	Side length

Returns

Matrix with L_{i+1, i} = 1, all other entries 0

Definition at line 4035 of file matrices.hpp.

MacWilliamsIdentity()

template<FiniteFieldType T>

Polynomial< InfInt > CECCO::MacWilliamsIdentity	(	const Polynomial< InfInt > &	A,
		size_t	n,
		size_t	k )

Definition at line 130 of file codes.hpp.

modinv()

template<uint16_t p, class T>

T CECCO::modinv ( T a )

constexpr

Multiplicative inverse modulo a prime.

Template Parameters

p	Prime modulus (must be prime for correct results)
T	Signed integer type

Parameters

a	Element to invert

Returns

Modular inverse a^(-1) mod p

Uses the extended Euclidean algorithm.

Definition at line 229 of file helpers.hpp.

Monomial()

template<CoefficientType T>

Polynomial< T > CECCO::Monomial ( size_t i, const T & a = T(1) )

constexpr

Monomial a · xⁱ

Parameters

i	Power of x
a	Coefficient (defaults to T(1)); a zero coefficient yields the zero polynomial

Definition at line 1375 of file polynomials.hpp.

normalize() [1/2]

template<CoefficientType T>
requires FieldType<T>

Polynomial< T > CECCO::normalize ( const Polynomial< T > & poly )

constexpr

Definition at line 1296 of file polynomials.hpp.

normalize() [2/2]

template<CoefficientType T>
requires FieldType<T>

Polynomial< T > CECCO::normalize ( Polynomial< T > && poly )

constexpr

Definition at line 1305 of file polynomials.hpp.

OnePolynomial()

template<CoefficientType T>

const Polynomial< T > & CECCO::OnePolynomial

(

)

Constant polynomial 1 (cached).

Definition at line 1390 of file polynomials.hpp.

operator!=() [1/4]

template<FieldType L, FieldType R>

bool CECCO::operator!=	(	const LinearCode< L > &	lhs,
		const LinearCode< R > &	rhs )

Definition at line 7106 of file codes.hpp.

operator!=() [2/4]

template<ReliablyComparableType T>

bool CECCO::operator!= ( const Matrix< T > & lhs, const Matrix< T > & rhs )

constexpr

Negation of operator==.

Returns

true iff dimensions or any component differ

Definition at line 3750 of file matrices.hpp.

operator!=() [3/4]

template<ReliablyComparableType T>

bool CECCO::operator!= ( const Polynomial< T > & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1319 of file polynomials.hpp.

operator!=() [4/4]

template<ReliablyComparableType T>

bool CECCO::operator!= ( const Vector< T > & lhs, const Vector< T > & rhs )

constexpr

Definition at line 1620 of file vectors.hpp.

operator%() [1/2]

template<CoefficientType T>

Polynomial< T > CECCO::operator% ( const Polynomial< T > & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1118 of file polynomials.hpp.

operator%() [2/2]

template<CoefficientType T>

Polynomial< T > CECCO::operator% ( Polynomial< T > && lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1125 of file polynomials.hpp.

operator*() [1/32]

template<ComponentType T>

Matrix< T > CECCO::operator* ( const Matrix< T > & lhs, const Matrix< T > & rhs )

constexpr

Definition at line 3036 of file matrices.hpp.

operator*() [2/32]

template<ComponentType T>

Matrix< T > CECCO::operator* ( const Matrix< T > & lhs, const T & rhs )

constexpr

Definition at line 3068 of file matrices.hpp.

operator*() [3/32]

template<CoefficientType T>

Polynomial< T > CECCO::operator* ( const Polynomial< T > & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1076 of file polynomials.hpp.

operator*() [4/32]

template<CoefficientType T>

Polynomial< T > CECCO::operator* ( const Polynomial< T > & lhs, const T & rhs )

constexpr

Definition at line 1132 of file polynomials.hpp.

operator*() [5/32]

template<CoefficientType T>

Polynomial< T > CECCO::operator* ( const Polynomial< T > & lhs, Polynomial< T > && rhs )

constexpr

Definition at line 1090 of file polynomials.hpp.

operator*() [6/32]

template<CoefficientType T>

Polynomial< T > CECCO::operator* ( const Polynomial< T > & lhs, size_t n )

constexpr

Definition at line 1175 of file polynomials.hpp.

operator*() [7/32]

template<ComponentType T>

Matrix< T > CECCO::operator* ( const T & lhs, const Matrix< T > & rhs )

constexpr

Definition at line 3086 of file matrices.hpp.

operator*() [8/32]

template<CoefficientType T>

Polynomial< T > CECCO::operator* ( const T & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1146 of file polynomials.hpp.

operator*() [9/32]

template<FieldType T>

T CECCO::operator* ( const T & lhs, const T & rhs )

constexpr

Definition at line 362 of file fields.hpp.

operator*() [10/32]

template<ComponentType T>

Vector< T > CECCO::operator* ( const T & lhs, const Vector< T > & rhs )

constexpr

Definition at line 1306 of file vectors.hpp.

operator*() [11/32]

template<FieldType T>

T CECCO::operator* ( const T & lhs, int rhs )

constexpr

Definition at line 390 of file fields.hpp.

operator*() [12/32]

template<ComponentType T>

Matrix< T > CECCO::operator* ( const T & lhs, Matrix< T > && rhs )

constexpr

Definition at line 3093 of file matrices.hpp.

operator*() [13/32]

template<CoefficientType T>

Polynomial< T > CECCO::operator* ( const T & lhs, Polynomial< T > && rhs )

constexpr

Definition at line 1153 of file polynomials.hpp.

operator*() [14/32]

template<FieldType T>

T CECCO::operator* ( const T & lhs, T && rhs )

constexpr

Definition at line 376 of file fields.hpp.

operator*() [15/32]

template<ComponentType T>

Vector< T > CECCO::operator* ( const T & lhs, Vector< T > && rhs )

constexpr

Definition at line 1313 of file vectors.hpp.

operator*() [16/32]

template<ComponentType T>

Vector< T > CECCO::operator* ( const Vector< T > & lhs, const Matrix< T > & rhs )

constexpr

Definition at line 3054 of file matrices.hpp.

operator*() [17/32]

template<ComponentType T>

Vector< T > CECCO::operator* ( const Vector< T > & lhs, const T & rhs )

constexpr

Definition at line 1288 of file vectors.hpp.

operator*() [18/32]

template<FieldType T>

T CECCO::operator* ( int lhs, const T & rhs )

constexpr

Definition at line 397 of file fields.hpp.

operator*() [19/32]

template<FieldType T>

T CECCO::operator* ( int lhs, T && rhs )

constexpr

Definition at line 411 of file fields.hpp.

operator*() [20/32]

template<ComponentType T>

Matrix< T > CECCO::operator* ( Matrix< T > && lhs, const Matrix< T > & rhs )

constexpr

Definition at line 3043 of file matrices.hpp.

operator*() [21/32]

template<ComponentType T>

Matrix< T > CECCO::operator* ( Matrix< T > && lhs, const T & rhs )

constexpr

Definition at line 3075 of file matrices.hpp.

operator*() [22/32]

template<CoefficientType T>

Polynomial< T > CECCO::operator* ( Polynomial< T > && lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1083 of file polynomials.hpp.

operator*() [23/32]

template<CoefficientType T>

Polynomial< T > CECCO::operator* ( Polynomial< T > && lhs, const T & rhs )

constexpr

Definition at line 1139 of file polynomials.hpp.

operator*() [24/32]

template<CoefficientType T>

Polynomial< T > CECCO::operator* ( Polynomial< T > && lhs, Polynomial< T > && rhs )

constexpr

Definition at line 1097 of file polynomials.hpp.

operator*() [25/32]

template<CoefficientType T>

Polynomial< T > CECCO::operator* ( Polynomial< T > && lhs, size_t n )

constexpr

Definition at line 1182 of file polynomials.hpp.

operator*() [26/32]

template<CoefficientType T>

Polynomial< T > CECCO::operator* ( size_t n, const Polynomial< T > & rhs )

constexpr

Definition at line 1189 of file polynomials.hpp.

operator*() [27/32]

template<CoefficientType T>

Polynomial< T > CECCO::operator* ( size_t n, Polynomial< T > && rhs )

constexpr

Definition at line 1196 of file polynomials.hpp.

operator*() [28/32]

template<FieldType T>

T CECCO::operator* ( T && lhs, const T & rhs )

constexpr

Definition at line 369 of file fields.hpp.

operator*() [29/32]

template<FieldType T>

T CECCO::operator* ( T && lhs, int rhs )

constexpr

Definition at line 404 of file fields.hpp.

operator*() [30/32]

template<FieldType T>

T CECCO::operator* ( T && lhs, T && rhs )

constexpr

Definition at line 383 of file fields.hpp.

operator*() [31/32]

template<ComponentType T>

Vector< T > CECCO::operator* ( Vector< T > && lhs, const Matrix< T > & rhs )

constexpr

Definition at line 3059 of file matrices.hpp.

operator*() [32/32]

template<ComponentType T>

Vector< T > CECCO::operator* ( Vector< T > && lhs, const T & rhs )

constexpr

Definition at line 1295 of file vectors.hpp.

operator+() [1/16]

template<ComponentType T>

Matrix< T > CECCO::operator+ ( const Matrix< T > & lhs, const Matrix< T > & rhs )

constexpr

Definition at line 2972 of file matrices.hpp.

operator+() [2/16]

template<ComponentType T>

Matrix< T > CECCO::operator+ ( const Matrix< T > & lhs, Matrix< T > && rhs )

constexpr

Definition at line 2986 of file matrices.hpp.

operator+() [3/16]

template<CoefficientType T>

Polynomial< T > CECCO::operator+ ( const Polynomial< T > & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1020 of file polynomials.hpp.

operator+() [4/16]

template<CoefficientType T>

Polynomial< T > CECCO::operator+ ( const Polynomial< T > & lhs, Polynomial< T > && rhs )

constexpr

Definition at line 1034 of file polynomials.hpp.

operator+() [5/16]

template<FieldType T>

T CECCO::operator+ ( const T & lhs, const T & rhs )

constexpr

Definition at line 306 of file fields.hpp.

operator+() [6/16]

template<FieldType T>

T CECCO::operator+ ( const T & lhs, T && rhs )

constexpr

Definition at line 320 of file fields.hpp.

operator+() [7/16]

template<ComponentType T>

Vector< T > CECCO::operator+ ( const Vector< T > & lhs, const Vector< T > & rhs )

constexpr

Definition at line 1224 of file vectors.hpp.

operator+() [8/16]

template<ComponentType T>

Vector< T > CECCO::operator+ ( const Vector< T > & lhs, Vector< T > && rhs )

constexpr

Definition at line 1238 of file vectors.hpp.

operator+() [9/16]

template<ComponentType T>

Matrix< T > CECCO::operator+ ( Matrix< T > && lhs, const Matrix< T > & rhs )

constexpr

Definition at line 2979 of file matrices.hpp.

operator+() [10/16]

template<ComponentType T>

Matrix< T > CECCO::operator+ ( Matrix< T > && lhs, Matrix< T > && rhs )

constexpr

Definition at line 2993 of file matrices.hpp.

operator+() [11/16]

template<CoefficientType T>

Polynomial< T > CECCO::operator+ ( Polynomial< T > && lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1027 of file polynomials.hpp.

operator+() [12/16]

template<CoefficientType T>

Polynomial< T > CECCO::operator+ ( Polynomial< T > && lhs, Polynomial< T > && rhs )

constexpr

Definition at line 1041 of file polynomials.hpp.

operator+() [13/16]

template<FieldType T>

T CECCO::operator+ ( T && lhs, const T & rhs )

constexpr

Definition at line 313 of file fields.hpp.

operator+() [14/16]

template<FieldType T>

T CECCO::operator+ ( T && lhs, T && rhs )

constexpr

Definition at line 327 of file fields.hpp.

operator+() [15/16]

template<ComponentType T>

Vector< T > CECCO::operator+ ( Vector< T > && lhs, const Vector< T > & rhs )

constexpr

Definition at line 1231 of file vectors.hpp.

operator+() [16/16]

template<ComponentType T>

Vector< T > CECCO::operator+ ( Vector< T > && lhs, Vector< T > && rhs )

constexpr

Definition at line 1245 of file vectors.hpp.

operator-() [1/16]

template<ComponentType T>

Matrix< T > CECCO::operator- ( const Matrix< T > & lhs, const Matrix< T > & rhs )

constexpr

Definition at line 3004 of file matrices.hpp.

operator-() [2/16]

template<ComponentType T>

Matrix< T > CECCO::operator- ( const Matrix< T > & lhs, Matrix< T > && rhs )

constexpr

Definition at line 3018 of file matrices.hpp.

operator-() [3/16]

template<CoefficientType T>

Polynomial< T > CECCO::operator- ( const Polynomial< T > & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1048 of file polynomials.hpp.

operator-() [4/16]

template<CoefficientType T>

Polynomial< T > CECCO::operator- ( const Polynomial< T > & lhs, Polynomial< T > && rhs )

constexpr

Definition at line 1062 of file polynomials.hpp.

operator-() [5/16]

template<FieldType T>

T CECCO::operator- ( const T & lhs, const T & rhs )

constexpr

Definition at line 334 of file fields.hpp.

operator-() [6/16]

template<FieldType T>

T CECCO::operator- ( const T & lhs, T && rhs )

constexpr

Definition at line 348 of file fields.hpp.

operator-() [7/16]

template<ComponentType T>

Vector< T > CECCO::operator- ( const Vector< T > & lhs, const Vector< T > & rhs )

constexpr

Definition at line 1256 of file vectors.hpp.

operator-() [8/16]

template<ComponentType T>

Vector< T > CECCO::operator- ( const Vector< T > & lhs, Vector< T > && rhs )

constexpr

Definition at line 1270 of file vectors.hpp.

operator-() [9/16]

template<ComponentType T>

Matrix< T > CECCO::operator- ( Matrix< T > && lhs, const Matrix< T > & rhs )

constexpr

Definition at line 3011 of file matrices.hpp.

operator-() [10/16]

template<ComponentType T>

Matrix< T > CECCO::operator- ( Matrix< T > && lhs, Matrix< T > && rhs )

constexpr

Definition at line 3025 of file matrices.hpp.

operator-() [11/16]

template<CoefficientType T>

Polynomial< T > CECCO::operator- ( Polynomial< T > && lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1055 of file polynomials.hpp.

operator-() [12/16]

template<CoefficientType T>

Polynomial< T > CECCO::operator- ( Polynomial< T > && lhs, Polynomial< T > && rhs )

constexpr

Definition at line 1069 of file polynomials.hpp.

operator-() [13/16]

template<FieldType T>

T CECCO::operator- ( T && lhs, const T & rhs )

constexpr

Definition at line 341 of file fields.hpp.

operator-() [14/16]

template<FieldType T>

T CECCO::operator- ( T && lhs, T && rhs )

constexpr

Definition at line 355 of file fields.hpp.

operator-() [15/16]

template<ComponentType T>

Vector< T > CECCO::operator- ( Vector< T > && lhs, const Vector< T > & rhs )

constexpr

Definition at line 1263 of file vectors.hpp.

operator-() [16/16]

template<ComponentType T>

Vector< T > CECCO::operator- ( Vector< T > && lhs, Vector< T > && rhs )

constexpr

Definition at line 1277 of file vectors.hpp.

operator/() [1/10]

template<CoefficientType T>

Matrix< T > CECCO::operator/ ( const Matrix< T > & lhs, const T & rhs )

constexpr

Definition at line 3104 of file matrices.hpp.

operator/() [2/10]

template<CoefficientType T>

Polynomial< T > CECCO::operator/ ( const Polynomial< T > & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1104 of file polynomials.hpp.

operator/() [3/10]

template<FieldType T>

Polynomial< T > CECCO::operator/ ( const Polynomial< T > & lhs, const T & rhs )

constexpr

Definition at line 1161 of file polynomials.hpp.

operator/() [4/10]

template<FieldType T>

T CECCO::operator/	(	const T &	lhs,
		const T &	rhs )

Definition at line 418 of file fields.hpp.

operator/() [5/10]

template<CoefficientType T>

Vector< T > CECCO::operator/ ( const Vector< T > & lhs, const T & rhs )

constexpr

Definition at line 1324 of file vectors.hpp.

operator/() [6/10]

template<CoefficientType T>

Matrix< T > CECCO::operator/ ( Matrix< T > && lhs, const T & rhs )

constexpr

Definition at line 3111 of file matrices.hpp.

operator/() [7/10]

template<CoefficientType T>

Polynomial< T > CECCO::operator/ ( Polynomial< T > && lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1111 of file polynomials.hpp.

operator/() [8/10]

template<FieldType T>

Polynomial< T > CECCO::operator/ ( Polynomial< T > && lhs, const T & rhs )

constexpr

Definition at line 1168 of file polynomials.hpp.

operator/() [9/10]

template<FieldType T>

T CECCO::operator/	(	T &&	lhs,
		const T &	rhs )

Definition at line 425 of file fields.hpp.

operator/() [10/10]

template<CoefficientType T>

Vector< T > CECCO::operator/ ( Vector< T > && lhs, const T & rhs )

constexpr

Definition at line 1331 of file vectors.hpp.

operator<<() [1/8]

template<FieldType T>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Code< T > &	rhs )

Definition at line 7121 of file codes.hpp.

operator<<() [2/8]

template<FiniteFieldType B, MOD modulus, LutMode mode>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Ext< B, modulus, mode > &	e )

Print as the integer label (or ERASURE_MARKER if erased).

Definition at line 3116 of file fields.hpp.

operator<<() [3/8]

template<uint16_t p>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Fp< p > &	e )

Print as the integer label (or ERASURE_MARKER if erased).

Definition at line 2196 of file fields.hpp.

operator<<() [4/8]

template<ComponentType T>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Matrix< T > &	rhs )

Pretty-print the matrix with column alignment and bracket borders.

Returns

Reference to os for chaining

Columns are separated by one blank, by three for polynomial components, whose own rendering contains blanks. An empty matrix is printed as "(empty matrix)".

Definition at line 3763 of file matrices.hpp.

operator<<() [5/8]

template<CoefficientType T>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Polynomial< T > &	rhs )

Definition at line 1324 of file polynomials.hpp.

operator<<() [6/8]

template<SignedIntType T>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Rationals< T > &	e )

Print as "numerator/denominator" (or just "numerator" when denominator is 1).

Single stream insertion for std::setw compatibility.

Definition at line 759 of file fields.hpp.

operator<<() [7/8]

template<FieldType T>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Trellis< T > &	Tr )

Definition at line 690 of file graphs.hpp.

operator<<() [8/8]

template<ComponentType T>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Vector< T > &	rhs )

Stream output as ( c₀, c₁, …, cₙ₋₁ ).

Definition at line 1639 of file vectors.hpp.

operator==() [1/4]

template<FieldType L, FieldType R>

bool CECCO::operator==	(	const LinearCode< L > &	lhs,
		const LinearCode< R > &	rhs )

Definition at line 7101 of file codes.hpp.

operator==() [2/4]

template<ReliablyComparableType T>

bool CECCO::operator== ( const Matrix< T > & lhs, const Matrix< T > & rhs )

constexpr

Equality of two matrices.

Returns

true iff dimensions match and all components are equal

Tag-aware fast paths handle structured operands (e.g. two Toeplitz matrices compare only their first row and column).

Definition at line 3703 of file matrices.hpp.

operator==() [3/4]

template<ReliablyComparableType T>

bool CECCO::operator== ( const Polynomial< T > & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1314 of file polynomials.hpp.

operator==() [4/4]

template<ReliablyComparableType T>

bool CECCO::operator== ( const Vector< T > & lhs, const Vector< T > & rhs )

constexpr

Definition at line 1615 of file vectors.hpp.

operator>>() [1/2]

template<class LHS, class RHS>

decltype(auto) CECCO::operator>>	(	LHS &&	lhs,
		RHS &&	rhs )

Function-call chaining: x >> f ≡ f(x).

Template Parameters

LHS	Input type
RHS	Callable on LHS

Parameters

lhs	Input value (perfect-forwarded)
rhs	Callable (perfect-forwarded)

Returns

rhs(lhs)

Selected when RHS is invocable with LHS. Disabled for std::ios_base-derived types to avoid clashing with stream operators. The companion overload below handles the case where the right-hand side is an assignment target.

Definition at line 1102 of file blocks.hpp.

operator>>() [2/2]

template<class LHS, class RHS>

RHS & CECCO::operator>>	(	LHS &&	lhs,
		RHS &	dst )

Assignment chaining: x >> dst ≡ dst = x; return dst.

Template Parameters

LHS	Input type
RHS	Assignment target type (assignable from LHS)

Parameters

lhs	Input value
dst	Destination variable

Returns

Reference to dst for continued chaining

Selected only when the callable overload above is not viable, so block calls always win over capture-into-variable when both are possible. Useful for capturing intermediate results in a chain (c >> map >> x >> awgn >> y >> demap >> r;).

Definition at line 1122 of file blocks.hpp.

operator^() [1/3]

template<CoefficientType T>

Polynomial< T > CECCO::operator^ ( const Polynomial< T > & base, int exponent )

constexpr

Polynomial exponentiation by square-and-multiply.

Returns

base^exponent

Warning

Does not follow C++ precedence for ^: in b * base ^ exponent the parser evaluates (b * base) ^ exponent. Parenthesise as b * (base ^ exponent), or call CECCO::sqm directly.

Exceptions

std::invalid_argument

if exponent is negative

Definition at line 1502 of file polynomials.hpp.

operator^() [2/3]

template<FieldType T>

T CECCO::operator^ ( const T & base, int exponent )

constexpr

Definition at line 432 of file fields.hpp.

operator^() [3/3]

template<FieldType T>

T CECCO::operator^ ( T && base, int exponent )

constexpr

Definition at line 437 of file fields.hpp.

pad_back() [1/2]

template<ComponentType T>

Vector< T > CECCO::pad_back ( const Vector< T > & v, size_t n )

constexpr

Definition at line 1513 of file vectors.hpp.

pad_back() [2/2]

template<ComponentType T>

Vector< T > CECCO::pad_back ( Vector< T > && v, size_t n )

constexpr

Definition at line 1520 of file vectors.hpp.

pad_front() [1/2]

template<ComponentType T>

Vector< T > CECCO::pad_front ( const Vector< T > & v, size_t n )

constexpr

Definition at line 1499 of file vectors.hpp.

pad_front() [2/2]

template<ComponentType T>

Vector< T > CECCO::pad_front ( Vector< T > && v, size_t n )

constexpr

Definition at line 1506 of file vectors.hpp.

PermutationMatrix()

template<ComponentType T>

Matrix< T > CECCO::PermutationMatrix

(

const std::vector< size_t > &

perm

)

Permutation matrix P with P_{i, perm[i]} = 1.

Parameters

perm	Permutation of {0, …, m-1}; m is inferred from perm.size()

Returns

m × m permutation matrix; the identity permutation returns IdentityMatrix

Exceptions

std::invalid_argument

if perm contains out-of-range or duplicate indices

Definition at line 3854 of file matrices.hpp.

PlotkinUpperBound()

template<FiniteFieldType T>

long double CECCO::PlotkinUpperBound	(	size_t	n,
		size_t	dmin )

Definition at line 100 of file code_bounds.hpp.

Here is the call graph for this function:

poly_long_div() [1/2]

template<CoefficientType T>

std::pair< Polynomial< T >, Polynomial< T > > CECCO::poly_long_div	(	const Polynomial< T > &	lhs,
		const Polynomial< T > &	rhs )

Definition at line 1203 of file polynomials.hpp.

poly_long_div() [2/2]

template<CoefficientType T>

std::pair< Polynomial< T >, Polynomial< T > > CECCO::poly_long_div	(	Polynomial< T > &&	lhs,
		const Polynomial< T > &	rhs )

Definition at line 1209 of file polynomials.hpp.

puncture() [1/3]

template<class C>

auto CECCO::puncture	(	C &&	code,
		size_t	i )

Definition at line 7066 of file codes.hpp.

puncture() [2/3]

template<FieldType T>

EmptyCode< T > CECCO::puncture	(	const EmptyCode< T > &	,
		const std::vector< size_t > &	)

Definition at line 7060 of file codes.hpp.

puncture() [3/3]

template<FieldType T>

LinearCode< T > CECCO::puncture	(	const LinearCode< T > &	C,
		const std::vector< size_t > &	v )

Definition at line 7041 of file codes.hpp.

randomize() [1/4]

template<CoefficientType T>

Matrix< T > CECCO::randomize

(

const Matrix< T > &

M

)

Definition at line 3118 of file matrices.hpp.

randomize() [2/4]

template<CoefficientType T>

Vector< T > CECCO::randomize

(

const Vector< T > &

v

)

Definition at line 1349 of file vectors.hpp.

randomize() [3/4]

template<CoefficientType T>

Matrix< T > CECCO::randomize

(

Matrix< T > &&

M

)

Definition at line 3125 of file matrices.hpp.

randomize() [4/4]

template<CoefficientType T>

Vector< T > CECCO::randomize

(

Vector< T > &&

v

)

Definition at line 1356 of file vectors.hpp.

reciprocal() [1/2]

template<CoefficientType T>

Polynomial< T > CECCO::reciprocal ( const Polynomial< T > & poly )

constexpr

Definition at line 1250 of file polynomials.hpp.

reciprocal() [2/2]

template<CoefficientType T>

Polynomial< T > CECCO::reciprocal ( Polynomial< T > && poly )

constexpr

Definition at line 1257 of file polynomials.hpp.

ReigerBurstUpperBound()

size_t CECCO::ReigerBurstUpperBound ( size_t n, size_t ell )

constexpr

Definition at line 224 of file code_bounds.hpp.

reverse() [1/2]

template<ComponentType T>

Vector< T > CECCO::reverse ( const Vector< T > & v )

constexpr

Definition at line 1555 of file vectors.hpp.

reverse() [2/2]

template<ComponentType T>

Vector< T > CECCO::reverse ( Vector< T > && v )

constexpr

Definition at line 1562 of file vectors.hpp.

reverse_columns() [1/2]

template<ComponentType T>

Matrix< T > CECCO::reverse_columns

(

const Matrix< T > &

M

)

Definition at line 3625 of file matrices.hpp.

reverse_columns() [2/2]

template<ComponentType T>

Matrix< T > CECCO::reverse_columns

(

Matrix< T > &&

M

)

Definition at line 3632 of file matrices.hpp.

reverse_rows() [1/2]

template<ComponentType T>

Matrix< T > CECCO::reverse_rows

(

const Matrix< T > &

M

)

Definition at line 3611 of file matrices.hpp.

reverse_rows() [2/2]

template<ComponentType T>

Matrix< T > CECCO::reverse_rows

(

Matrix< T > &&

M

)

Definition at line 3618 of file matrices.hpp.

rotate_left() [1/2]

template<ComponentType T>

Vector< T > CECCO::rotate_left ( const Vector< T > & v, size_t i )

constexpr

Definition at line 1527 of file vectors.hpp.

rotate_left() [2/2]

template<ComponentType T>

Vector< T > CECCO::rotate_left ( Vector< T > && v, size_t i )

constexpr

Definition at line 1534 of file vectors.hpp.

rotate_right() [1/2]

template<ComponentType T>

Vector< T > CECCO::rotate_right ( const Vector< T > & v, size_t i )

constexpr

Definition at line 1541 of file vectors.hpp.

rotate_right() [2/2]

template<ComponentType T>

Vector< T > CECCO::rotate_right ( Vector< T > && v, size_t i )

constexpr

Definition at line 1548 of file vectors.hpp.

rref() [1/2]

template<FieldType T>

Matrix< T > CECCO::rref

(

const Matrix< T > &

M

)

Definition at line 3667 of file matrices.hpp.

rref() [2/2]

template<FieldType T>

Matrix< T > CECCO::rref

(

Matrix< T > &&

M

)

Definition at line 3674 of file matrices.hpp.

scale_column() [1/2]

template<ComponentType T>

Matrix< T > CECCO::scale_column	(	const Matrix< T > &	M,
		const T &	s,
		size_t	i )

Definition at line 3334 of file matrices.hpp.

scale_column() [2/2]

template<ComponentType T>

Matrix< T > CECCO::scale_column	(	Matrix< T > &&	M,
		const T &	s,
		size_t	i )

Definition at line 3348 of file matrices.hpp.

scale_row() [1/2]

template<ComponentType T>

Matrix< T > CECCO::scale_row	(	const Matrix< T > &	M,
		const T &	s,
		size_t	i )

Definition at line 3327 of file matrices.hpp.

scale_row() [2/2]

template<ComponentType T>

Matrix< T > CECCO::scale_row	(	Matrix< T > &&	M,
		const T &	s,
		size_t	i )

Definition at line 3341 of file matrices.hpp.

Schur_product()

template<ComponentType T>

Vector< T > CECCO::Schur_product	(	const Vector< T > &	lhs,
		const Vector< T > &	rhs )

Schur (component-wise) product.

Exceptions

std::invalid_argument

if lengths differ

Definition at line 1603 of file vectors.hpp.

set_component() [1/4]

template<ComponentType T>

Matrix< T > CECCO::set_component	(	const Matrix< T > &	M,
		size_t	i,
		size_t	j,
		const T &	c )

Definition at line 3182 of file matrices.hpp.

set_component() [2/4]

template<ComponentType T>

Vector< T > CECCO::set_component	(	const Vector< T > &	v,
		size_t	i,
		const T &	c )

Definition at line 1363 of file vectors.hpp.

set_component() [3/4]

template<ComponentType T>

Matrix< T > CECCO::set_component	(	Matrix< T > &&	M,
		size_t	i,
		size_t	j,
		const T &	c )

Definition at line 3189 of file matrices.hpp.

set_component() [4/4]

template<ComponentType T>

Vector< T > CECCO::set_component	(	Vector< T > &&	v,
		size_t	i,
		const T &	c )

Definition at line 1370 of file vectors.hpp.

set_submatrix() [1/2]

template<ComponentType T>

Matrix< T > CECCO::set_submatrix	(	const Matrix< T > &	M,
		size_t	i,
		size_t	j,
		const Matrix< T > &	N )

Definition at line 3201 of file matrices.hpp.

set_submatrix() [2/2]

template<ComponentType T>

Matrix< T > CECCO::set_submatrix	(	Matrix< T > &&	M,
		size_t	i,
		size_t	j,
		const Matrix< T > &	N )

Definition at line 3208 of file matrices.hpp.

set_subvector() [1/2]

template<ComponentType T>

Vector< T > CECCO::set_subvector ( Vector< T > && v, size_t start, const Vector< T > & w )

constexpr

Definition at line 1392 of file vectors.hpp.

set_subvector() [2/2]

template<ComponentType T>

Vector< T > CECCO::set_subvector ( Vector< T > v, size_t start, const Vector< T > & w )

constexpr

Definition at line 1387 of file vectors.hpp.

shift_down() [1/2]

template<CoefficientType T>

Polynomial< T > CECCO::shift_down ( const Polynomial< T > & poly, size_t s )

constexpr

Definition at line 1282 of file polynomials.hpp.

shift_down() [2/2]

template<CoefficientType T>

Polynomial< T > CECCO::shift_down ( Polynomial< T > && poly, size_t s )

constexpr

Definition at line 1289 of file polynomials.hpp.

shift_up() [1/2]

template<CoefficientType T>
requires ReliablyComparableType<T>

Polynomial< T > CECCO::shift_up ( const Polynomial< T > & poly, size_t s )

constexpr

Definition at line 1264 of file polynomials.hpp.

shift_up() [2/2]

template<CoefficientType T>
requires ReliablyComparableType<T>

Polynomial< T > CECCO::shift_up ( Polynomial< T > && poly, size_t s )

constexpr

Definition at line 1273 of file polynomials.hpp.

shorten()

template<class B>

auto CECCO::shorten	(	B &&	base,
		size_t	j,
		size_t	i )

Definition at line 7096 of file codes.hpp.

showall()

std::ostream & CECCO::showall ( std::ostream & os )

inline

Definition at line 199 of file codes.hpp.

showbasic()

std::ostream & CECCO::showbasic ( std::ostream & os )

inline

Definition at line 189 of file codes.hpp.

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showmost()

std::ostream & CECCO::showmost ( std::ostream & os )

inline

Definition at line 194 of file codes.hpp.

showspecial()

std::ostream & CECCO::showspecial ( std::ostream & os )

inline

Definition at line 204 of file codes.hpp.

SingletonUpperBound()

size_t CECCO::SingletonUpperBound ( size_t n, size_t dmin )

inline

Definition at line 143 of file code_bounds.hpp.

sqm()

template<class T>

T CECCO::sqm ( T b, int e )

constexpr

Exponentiation by square-and-multiply.

Template Parameters

T	Type supporting multiplication and, for negative exponents, division

Parameters

b	Base value
e	Exponent

Returns

b^e

For negative exponents, computes (1/b)^|e|.

Note

Returns T(1) for e = 0.

Exceptions

std::overflow_error	if T is an integral type and the result would overflow it
std::invalid_argument	for negative exponents when T is integral or has no division

Definition at line 376 of file helpers.hpp.

SubfieldSubcode() [1/2]

template<class B>

CECCO::SubfieldSubcode

(

B &&

)

-> SubfieldSubcode< B >

SubfieldSubcode() [2/2]

template<class B>

CECCO::SubfieldSubcode

(

const B &

)

-> SubfieldSubcode< B >

supp()

template<ReliablyComparableType T>

std::vector< size_t > CECCO::supp

(

const Vector< T > &

v

)

Support; see Vector::supp for semantics.

Definition at line 1662 of file vectors.hpp.

swap_columns() [1/2]

template<ComponentType T>

Matrix< T > CECCO::swap_columns	(	const Matrix< T > &	M,
		size_t	i,
		size_t	j )

Definition at line 3306 of file matrices.hpp.

swap_columns() [2/2]

template<ComponentType T>

Matrix< T > CECCO::swap_columns	(	Matrix< T > &&	M,
		size_t	i,
		size_t	j )

Definition at line 3320 of file matrices.hpp.

swap_rows() [1/2]

template<ComponentType T>

Matrix< T > CECCO::swap_rows	(	const Matrix< T > &	M,
		size_t	i,
		size_t	j )

Definition at line 3299 of file matrices.hpp.

swap_rows() [2/2]

template<ComponentType T>

Matrix< T > CECCO::swap_rows	(	Matrix< T > &&	M,
		size_t	i,
		size_t	j )

Definition at line 3313 of file matrices.hpp.

to_long_double()

long double CECCO::to_long_double ( const InfInt & v )

inline

Conversion of an InfInt of arbitrary magnitude to long double.

Parameters

v

Integer

Returns

Nearest representable value (about 18 significant decimal digits are preserved)

Definition at line 316 of file helpers.hpp.

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ToeplitzMatrix()

template<ComponentType T>

Matrix< T > CECCO::ToeplitzMatrix ( const Vector< T > & v, size_t m, size_t n )

constexpr

m × n Toeplitz matrix from its diagonal entries

Parameters

v	Diagonal values, ordered so that v[i − j + n − 1] sits on entry (i, j); length m + n − 1
m	Number of rows
n	Number of columns

Returns

Toeplitz matrix; tagged by the strongest detected structural type

Exceptions

std::invalid_argument	if m == 0 or n == 0
std::invalid_argument	if v.length() != m + n - 1

Definition at line 3934 of file matrices.hpp.

transpose() [1/2]

template<ComponentType T>

Matrix< T > CECCO::transpose ( const Matrix< T > & M )

constexpr

Definition at line 3653 of file matrices.hpp.

transpose() [2/2]

template<ComponentType T>

Matrix< T > CECCO::transpose ( Matrix< T > && M )

constexpr

Definition at line 3660 of file matrices.hpp.

unaugment()

template<FieldType T, class B>

B CECCO::unaugment

(

const AugmentedCode< T, B > &

C

)

Definition at line 7011 of file codes.hpp.

unerase_column() [1/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_column ( const Matrix< T > & lhs, size_t i )

constexpr

Definition at line 3539 of file matrices.hpp.

unerase_column() [2/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_column ( Matrix< T > && lhs, size_t i )

constexpr

Definition at line 3546 of file matrices.hpp.

unerase_columns() [1/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_columns ( const Matrix< T > & lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3525 of file matrices.hpp.

unerase_columns() [2/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_columns ( Matrix< T > && lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3532 of file matrices.hpp.

unerase_component() [1/4]

template<ComponentType T>

Matrix< T > CECCO::unerase_component ( const Matrix< T > & lhs, size_t i, size_t j )

constexpr

Definition at line 3483 of file matrices.hpp.

unerase_component() [2/4]

template<ComponentType T>

Vector< T > CECCO::unerase_component	(	const Vector< T > &	lhs,
		size_t	i )

Definition at line 1483 of file vectors.hpp.

unerase_component() [3/4]

template<ComponentType T>

Matrix< T > CECCO::unerase_component ( Matrix< T > && lhs, size_t i, size_t j )

constexpr

Definition at line 3490 of file matrices.hpp.

unerase_component() [4/4]

template<ComponentType T>

Vector< T > CECCO::unerase_component	(	Vector< T > &&	lhs,
		size_t	i )

Definition at line 1490 of file vectors.hpp.

unerase_components() [1/2]

template<ComponentType T>

Vector< T > CECCO::unerase_components	(	const Vector< T > &	lhs,
		const std::vector< size_t > &	v )

Definition at line 1469 of file vectors.hpp.

unerase_components() [2/2]

template<ComponentType T>

Vector< T > CECCO::unerase_components	(	Vector< T > &&	lhs,
		const std::vector< size_t > &	v )

Definition at line 1476 of file vectors.hpp.

unerase_row() [1/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_row ( const Matrix< T > & lhs, size_t i )

constexpr

Definition at line 3595 of file matrices.hpp.

unerase_row() [2/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_row ( Matrix< T > && lhs, size_t i )

constexpr

Definition at line 3602 of file matrices.hpp.

unerase_rows() [1/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_rows ( const Matrix< T > & lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3581 of file matrices.hpp.

unerase_rows() [2/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_rows ( Matrix< T > && lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3588 of file matrices.hpp.

unextend()

template<FieldType T, class B>

B CECCO::unextend

(

const ExtendedCode< T, B > &

C

)

Definition at line 6997 of file codes.hpp.

unit_vector()

template<ComponentType T>

Vector< T > CECCO::unit_vector	(	size_t	length,
		size_t	i )

Length-length vector with T(1) at index i and zeros elsewhere.

Exceptions

std::invalid_argument

if i >= length

Definition at line 1629 of file vectors.hpp.

unlengthen()

template<FieldType T, class D>

auto CECCO::unlengthen

(

const ExtendedCode< T, AugmentedCode< T, D > > &

C

)

Definition at line 7031 of file codes.hpp.

UpperBound()

template<FiniteFieldType T>

long double CECCO::UpperBound	(	size_t	n,
		size_t	dmin )

Definition at line 181 of file code_bounds.hpp.

UpperShiftMatrix()

template<ComponentType T>

Matrix< T > CECCO::UpperShiftMatrix ( size_t m )

constexpr

m × m upper shift matrix (ones on the superdiagonal)

Parameters

m	Side length

Returns

Matrix with U_{i, i+1} = 1, all other entries 0

Definition at line 4021 of file matrices.hpp.

VandermondeMatrix()

template<ReliablyComparableType T>

Matrix< T > CECCO::VandermondeMatrix ( const Vector< T > & v, size_t m )

constexpr

Vandermonde matrix V_{i, j} = v[j]^i.

Parameters

v	Evaluation points; must be pairwise distinct
m	Number of rows (i.e. the highest power is m − 1)

Returns

m × v.length() Vandermonde matrix; the 1 × 1 case is tagged as details::Identity

Exceptions

std::invalid_argument

if v is empty, has duplicates, or m is zero

Definition at line 3989 of file matrices.hpp.

Vector()

template<CoefficientType T>

CECCO::Vector

(

const Polynomial< T > &

)

-> Vector< T >

Deduction guide: a vector constructed from a polynomial deduces the coefficient type.

vertical_join() [1/3]

template<ComponentType T>

Matrix< T > CECCO::vertical_join	(	const Matrix< T > &	lhs,
		const Matrix< T > &	rhs )

Definition at line 3236 of file matrices.hpp.

vertical_join() [2/3]

template<ComponentType T>

Matrix< T > CECCO::vertical_join	(	Matrix< T > &&	lhs,
		const Matrix< T > &	rhs )

Definition at line 3243 of file matrices.hpp.

vertical_join() [3/3]

template<ComponentType T>

Matrix< T > CECCO::vertical_join	(	Matrix< T > &&	lhs,
		Matrix< T > &&	rhs )

Definition at line 3250 of file matrices.hpp.

wH() [1/2]

template<ReliablyComparableType T>

size_t CECCO::wH ( const Matrix< T > & M )

constexpr

Definition at line 3132 of file matrices.hpp.

wH() [2/2]

template<ReliablyComparableType T>

size_t CECCO::wH ( const Vector< T > & v )

constexpr

Hamming weight; see Vector::wH for semantics.

Definition at line 1656 of file vectors.hpp.

ZeroMatrix()

template<ComponentType T>

Matrix< T > CECCO::ZeroMatrix ( size_t m, size_t n )

constexpr

m × n matrix of zeros (tag details::Zero)

Parameters

m	Number of rows
n	Number of columns

Returns

Newly constructed zero matrix

Definition at line 3827 of file matrices.hpp.

ZeroPolynomial()

template<CoefficientType T>

const Polynomial< T > & CECCO::ZeroPolynomial

(

)

Constant polynomial 0 (cached).

Definition at line 1383 of file polynomials.hpp.

Variable Documentation

ERASURE_MARKER

std::string_view CECCO::ERASURE_MARKER = "X"

inlineconstexpr

Definition at line 444 of file fields.hpp.