65.39 IsSelfOrthogonalCode

IsSelfOrthogonalCode( C )

IsSelfOrthogonalCode returns true if C is self-orthogonal. A code is self-orthogonal if every element of C is orthogonal to all elements of C, including itself. In the linear case, this simply means that the generator matrix of C multiplied with its transpose yields a null matrix.

In addition, a code is self-dual if it contains all vectors that its elements are orthogonal to (see IsSelfDualCode).

    gap> R := ReedMullerCode(1,4);
    a linear [16,5,8]6 Reed-Muller (1,4) code over GF(2)
    gap> IsSelfOrthogonalCode(R);
    true
    gap> IsSelfDualCode(R);
    false 

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