65.98 ConstructionBCode

ConstructionBCode( C )

The function ConstructionBCode takes a binary linear code C and calculates the minimum distance of the dual of C (see DualCode). It then removes the columns of the parity check matrix of C where a codeword of the dual code of minimal weight has coordinates unequal to zero. the resulting matrix is a parity check matrix for an [n-dd, k-dd+1, geq d] code, where dd is the minimum distance of the dual of C.

    gap> C1 := ReedMullerCode( 2, 5 );
    a linear [32,16,8]6 Reed-Muller (2,5) code over GF(2)
    gap> C2 := ConstructionBCode( C1 );
    a linear [24,9,8]5..10 Construction B (8 coordinates)
    gap> BoundsMinimumDistance( 24, 9, GF(2) );
    an optimal linear [24,9,d] code over GF(2) has d=8  # so C2 is optimal

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