65.100 ConversionFieldCode

ConversionFieldCode( C )

ConversionFieldCode returns code C after converting its field. If the field of C is GF(q^m), the returned code has field GF(q). Each symbol of every codeword is replaced by a concatenation of m symbols from GF(q). If C is an (n, M, d_1) code, the returned code is a (n*m, M, d_2) code, where d_2 > d_1.

See also HorizontalConversionFieldMat.

    gap> R := RepetitionCode( 4, GF(4) );
    a cyclic [4,1,4]3 repetition code over GF(4)
    gap> R2 := ConversionFieldCode( R );
    a linear [8,2,4]3..4 code, converted to basefield GF(2)
    gap> Size( R ) = Size( R2 );
    true
    gap> GeneratorMat( R );
    [ [ Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ] ]
    gap> GeneratorMat( R2 );
    [ [ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2) ],
      [ 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0 ] ] 

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