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
construction. It uses the information in this field to
construct a code. This form is meant to be used together with the
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
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