65.113 UpperBoundJohnson

UpperBoundJohnson( n, d )

The Johnson bound is an improved version of the Hamming bound (see UpperBoundHamming). In addition to the Hamming bound, it takes into account the elements of the space outside the balls of radius e around the elements of the code. The Johnson bound only works for binary codes.

    gap> UpperBoundJohnson( 13, 5 );
    77
    gap> UpperBoundHamming( 13, 5, 2);
    89   # in this case the Johnson bound is better 

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