65.97 ResidueCode

ResidueCode( C [, w ] )

The function ResidueCode takes a codeword c of C of weight w (if w is omitted, a codeword of minimal weight is used). C must be a linear code and w must be greater than zero. It removes this word and all its linear combinations from the code and then punctures the code in the coordinates where c is unequal to zero. The resulting code is an [n-w, k-1, d-lfloor w*(q-1)/q rfloor ] code.

    gap> C1 := BCHCode( 15, 7 );
    a cyclic [15,5,7]5 BCH code, delta=7, b=1 over GF(2)
    gap> C2 := ResidueCode( C1 );
    a linear [8,4,4]2 residue code
    gap> c := Codeword( [ 0,0,0,1,0,0,1,1,0,1,0,1,1,1,1 ], C1);;
    gap> C3 := ResidueCode( C1, c );
    a linear [7,4,3]1 residue code 

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