65.106 DirectProductCode

DirectProductCode( C_1, C_2 )

DirectProductCode returns the direct product of codes C_1 and C_2. Both must be linear codes. Suppose C_i has generator matrix G_i. The direct product of C_1 and C_2 then has the Kronecker product of G_1 and G_2 as the generator matrix (see KroneckerProduct).

If C_i is a [n_i, k_i, d_i] code, the direct product then is a [n_1*n_2,k_1*k_2,d_1*d_2] code.

    gap> L1 := LexiCode(10, 4, GF(2));
    a linear [10,5,4]2..4 lexicode over GF(2)
    gap> L2 := LexiCode(8, 3, GF(2));
    a linear [8,4,3]2..3 lexicode over GF(2)
    gap> D := DirectProductCode(L1, L2);
    a linear [80,20,12]20..45 direct product code 

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