65.19 Comparisons of Codes

C_1 = C_2
C_1 < C_2

The equality operator = evaluates to true if the codes C_1 and C_2 are equal, and to false otherwise. The inequality operator < evaluates to true if the codes C_1 and C_2 are not equal, and to false otherwise.

Note that codes are equal if and only if their elements are equal. Codes can also be compared with objects of other types. Of course they are never equal.

    gap> M := [ [0, 0], [1, 0], [0, 1], [1, 1] ];;
    gap> C1 := ElementsCode( M, GF(2) );
    a (2,4,1..2)0 user defined unrestricted code over GF(2)
    gap> M = C1;
    false
    gap> C2 := GeneratorMatCode( [ [1, 0], [0, 1] ], GF(2) );
    a linear [2,2,1]0 code defined by generator matrix over GF(2)
    gap> C1 = C2;
    true
    gap> ReedMullerCode( 1, 3 ) = HadamardCode( 8 );
    true
    gap> WholeSpaceCode( 5, GF(4) ) = WholeSpaceCode( 5, GF(2) );
    false 

Another way of comparing codes is IsEquivalent, which checks if two codes are equi-valent (see IsEquivalent).

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