65.116 UpperBoundGriesmer

UpperBoundGriesmer( n, d, q )

The Griesmer bound is valid only for linear codes. It is obtained by counting the number of equal symbols in each row of the generator matrix of the code. By omitting the coordinates in which all rows have a zero, a smaller code results. The Griesmer bound is obtained by repeating this proces until a trivial code is left in the end.

    gap> UpperBoundGriesmer( 13, 5, 2 );
    64
    gap> UpperBoundGriesmer( 18, 9, 2 );
    8        # the maximum number of words for a linear code is 8
    gap> Size( PuncturedCode( HadamardCode( 20, 1 ) ) );
    20       # this non-linear code has 20 elements 

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