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
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
Previous Up Top Next