65.71 BestKnownLinearCode

BestKnownLinearCode( n, k , F )

BestKnownLinearCode returns the best known linear code of length n, dimension k over field F. The function uses the tables described in section BoundsMinimumDistance to construct this code.

    gap> C1 := BestKnownLinearCode( 23, 12, GF(2) );
    a cyclic [23,12,7]3 binary Golay code over GF(2)
    gap> C1 = BinaryGolayCode();
    true
    gap> Display( BestKnownLinearCode( 8, 4, GF(4) ) );
    a linear [8,4,4]2..3 U

U+V construction code of
    U: a cyclic [4,3,2]1 dual code of
       a cyclic [4,1,4]3 repetition code over GF(4)
    V: a cyclic [4,1,4]3 repetition code over GF(4)
    gap> C := BestKnownLinearCode(131,47);
    a linear [131,47,28..32]23..68 shortened code 

BestKnownLinearCode( rec )

In this form, rec must be a record containing the fields lowerBound, upperBound and construction. It uses the information in this field to construct a code. This form is meant to be used together with the function BoundsMinimumDistance (see BoundsMinimumDistance), if the bounds are already calculated.

    gap> bounds := BoundsMinimumDistance( 20, 17, GF(4) );
    an optimal linear [20,17,d] code over GF(4) has d=3
    gap> C := BestKnownLinearCode( bounds );
    a linear [20,17,3]2 shortened code
    gap> C = BestKnownLinearCode( 20, 17, GF(4) );
    true 

Previous Up Top Next
Index