Invariants

# C: Code -> RngIntElt

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

C . i: Code, RngIntElt -> ModTupRngElt

Name(C, i): 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 the code \(C\), 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 \(C\).

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 a length \(n\) code \(C\) over a ring \(R\), return the generic \((n, \#R^n, 1)\) code in which \(C\) is contained.

Length(C): Code -> RngIntElt

Given a code \(C\), return the block length \(n\) of \(C\).

PseudoDimension(C): Code -> RngIntElt

NumberOfGenerators(C): Code -> RngIntElt

Ngens(C): Code -> RngIntElt

The number of generators (which equals the pseudo-dimension \(k\)) of the 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 the code \(C\).

RSpace(C): Code -> ModTupRng

Given a length \(n\) 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

Given a code \(C\) over a ring with cardinality \(q\), return the information rate of \(C\), that is, the ratio \(Log_q(\#C)/n\).