65.107 IntersectionCode

IntersectionCode( C_1, C_2 )

IntersectionCode returns the intersection of codes C_1 and C_2. This code consists of all codewords that are both in C_1 and C_2. If both codes are linear, the result is also linear. If both are cyclic, the result is also cyclic.

    gap> C := CyclicCodes(7, GF(2));
    [ a cyclic [7,7,1]0 enumerated code over GF(2),
      a cyclic [7,6,1..2]1 enumerated code over GF(2),
      a cyclic [7,3,1..4]2..3 enumerated code over GF(2),
      a cyclic [7,0,7]7 enumerated code over GF(2),
      a cyclic [7,3,1..4]2..3 enumerated code over GF(2),
      a cyclic [7,4,1..3]1 enumerated code over GF(2),
      a cyclic [7,1,7]3 enumerated code over GF(2),
      a cyclic [7,4,1..3]1 enumerated code over GF(2) ]
    gap> IntersectionCode(C[6], C[8]) = C[7];
    true 

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