65.108 UnionCode

UnionCode( C_1, C_2 )

UnionCode returns the union of codes C_1 and C_2. This code consists of the union of all codewords of C_1 and C_2 and all linear combinations. Therefore this function works only for linear codes. The function AddedElementsCode can be used for non-linear codes, or if the resulting code should not include linear combinations. See AddedElementsCode. If both arguments are cyclic, the result is also cyclic.

    gap> G := GeneratorMatCode([[1,0,1],[0,1,1]]*Z(2)^0, GF(2));
    a linear [3,2,1..2]1 code defined by generator matrix over GF(2)
    gap> H := GeneratorMatCode([[1,1,1]]*Z(2)^0, GF(2));
    a linear [3,1,3]1 code defined by generator matrix over GF(2)
    gap> U := UnionCode(G, H);
    a linear [3,3,1]0 union code
    gap> c := Codeword("010");; c in G;
    false
    gap> c in H;
    false
    gap> c in U;
    true 

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