Boolean Predicates

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

u in C : ModTupRngElt, Code -> BoolElt

Return true if and only if the vector u of V belongs to the code C.

u notin C : ModTupRngElt, Code -> BoolElt

Return true if and only if the vector u of V does not belong to the code C.

C subset D : Code, Code -> BoolElt

Return true if and only if the code C is a subcode of the code D.

C notsubset D : Code, Code -> BoolElt

Return true if and only if the code C is not a subcode of the code D.

C eq D : Code, Code -> BoolElt

Return true if and only if the codes C and D are equal.

C ne D : Code, Code -> BoolElt

Return true if and only if the codes C and D are not equal.

IsCyclic(C) : Code -> BoolElt

Return true if and only if the linear code C is a cyclic code.

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; that is, return whether C is contained in the dual of C.

IsProjective(C) : Code -> BoolElt

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

IsZero(u) : ModTupRngElt -> BoolElt

Return true if and only if the codeword u is the zero vector.

> Z4 := IntegerRing(4);
> K8 := LinearCode< Z4, 8 |
>     [1,1,1,1,1,1,1,1],
>     [0,2,0,0,0,0,0,2],
>     [0,0,2,0,0,0,0,2],
>     [0,0,0,2,0,0,0,2],
>     [0,0,0,0,2,0,0,2],
>     [0,0,0,0,0,2,0,2],
>     [0,0,0,0,0,0,2,2]>;
> K8;
[8, 7, 2] Linear Code over IntegerRing(4)
Generator matrix:
[1 1 1 1 1 1 1 1]
[0 2 0 0 0 0 0 2]
[0 0 2 0 0 0 0 2]
[0 0 0 2 0 0 0 2]
[0 0 0 0 2 0 0 2]
[0 0 0 0 0 2 0 2]
[0 0 0 0 0 0 2 2]
> IsCyclic(K8);
true
> IsSelfDual(K8);
true
> K8 eq Dual(K8);
true