Properties of Codes

For the following operators, \(C\) and \(D\) are codes defined as a subset (or subspace) of the vector space \(V\).

IsSelfDual(C): Code -> BoolElt

Return true if and only if the linear code \(C\) is self-dual (or self-orthogonal) (i.e. \(C\) equals the dual of \(C\)).

IsSelfOrthogonal(C): Code -> BoolElt

Return true if and only if the linear code \(C\) is self-orthogonal (i.e. \(C\) is contained in the dual of \(C\)).

IsPerfect(C): Code -> BoolElt

Return true if and only if the linear code \(C\) is perfect; that is, if and only if the cardinality of \(C\) is equal to the size of the sphere packing bound of \(C\).

IsProjective(C): Code -> BoolElt

Returns true if and only if the (non-quantum) code \(C\) is projective over its alphabet.

IsAdditiveProjective(C): CodeAdd -> BoolElt

Returns true if and only if the additive code \(C\) is projective over its coefficient field. It is possible that some of the columns may not be independent with respect to the alphabet of the code.