65.102 ConstantWeightSubcode

ConstantWeightSubcode( C, w )

ConstantWeightSubcode returns the subcode of C that only has codewords of weight w. The resulting code is a non-linear code, because it does not contain the all-zero vector.

    gap> N := NordstromRobinsonCode();; WeightDistribution(N);
    [ 1, 0, 0, 0, 0, 0, 112, 0, 30, 0, 112, 0, 0, 0, 0, 0, 1 ]
    gap> C := ConstantWeightSubcode(N, 8);
    a (16,30,6..16)5..8 code with codewords of weight 8
    gap> WeightDistribution(C);
    [ 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0 ] 

ConstantWeightSubcode( C )

In this format, ConstantWeightSubcode returns the subcode of C consisting of all minimum weight codewords of C.

    gap> E := ExtendedTernaryGolayCode();; WeightDistribution(E);
    [ 1, 0, 0, 0, 0, 0, 264, 0, 0, 440, 0, 0, 24 ]
    gap> C := ConstantWeightSubcode(E);
    a (12,264,6..12)3..6 code with codewords of weight 6
    gap> WeightDistribution(C);
    [ 0, 0, 0, 0, 0, 0, 264, 0, 0, 0, 0, 0, 0 ] 

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