Invariants of Codes

# C : Code -> RngIntElt

Given a code C, return the number of codewords belonging to C.

C . i : Code, RngIntElt -> ModTupRngElt

Name(C, d) : Code, RngIntElt -> ModTupRngElt

Given a code C and a positive integer i, return the i-th generator of C.

Alphabet(C) : Code -> Rng

The underlying ring (or alphabet) R of the code C.

AmbientSpace(C) : Code -> ModTupRng

The ambient space of C, i.e., the generic R-space V in which C is contained.

Basis(C) : Code -> [ ModTupRngElt ]

The basis of the linear code C, returned as a sequence of elements of C.

Dimension(C) : Code -> RngIntElt

The pseudo-dimension k of the [n, k] linear code C. This is the number of rows in the generator matrix, which gives a unique canonical generating set for the code.

Generators(C) : Code -> { ModTupRngElt }

The generators for the linear code C, returned as a set.

GeneratorMatrix(C) : Code -> ModMatRngElt

The generator matrix for the linear code C. This gives a unique canonical generating set for the code.

Generic(C) : Code -> Code

Given an [n, k] code C, return the generic [n, n, 1] code in which C is contained.

Length(C) : Code -> RngIntElt

Given an [n, k] code C, return the block length n of C.

NumberOfGenerators(C) : Code -> RngIntElt

Ngens(C) : Code -> RngIntElt

The number of generators (which equals the pseudo-dimension k) of the [n, k] linear code C.

ParityCheckMatrix(C) : Code -> ModMatRngElt

The parity check matrix for the code C, which can be defined as the canonical generator matrix of the dual of C.

Random(C): Code -> ModTupRngElt

A random codeword of C.

RSpace(C) : Code -> ModTupRng

Given an [n, k] linear code C, defined as a subspace U of the n-dimensional space V, return U as a subspace of V with basis corresponding to the rows of the generator matrix for C.

InformationRate(C) : Code -> RngPrElt

The information rate of the [n, k] code C. This is the ratio k/n.