65.93 RemovedElementsCode

RemovedElementsCode( C, L )

RemovedElementsCode returns code C after removing a list of codewords L from its elements. L must be a list of codeword input. The result is an unrestricted code.

    gap> C1 := HammingCode( 4 );; WeightDistribution( C1 );
    [ 1, 0, 0, 35, 105, 168, 280, 435, 435, 280, 168, 105, 35, 0, 0, 1 ]
    gap> L := Filtered( Elements(C1), i -> WeightCodeword(i) = 3 );;
    gap> C2 := RemovedElementsCode( C1, L );
    a (15,2013,3..15)2..15 code with 35 word(s) removed
    gap> WeightDistribution( C2 );
    [ 1, 0, 0, 0, 105, 168, 280, 435, 435, 280, 168, 105, 35, 0, 0, 1 ]
    gap> MinimumDistance( C2 );
    3        # C2 is not linear, so the minimum weight does not have to
             # be equal to the minimum distance 

Adding elements to a code is done by the function AddedElementsCode (see AddedElementsCode). To remove codewords from the base of a linear code, use ExpurgatedCode (see ExpurgatedCode).

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