UpperBoundElias( n, d, q )
The Elias bound is an improvement of the Plotkin bound (see UpperBoundPlotkin) for large codes. Subcodes are used to decrease the size of the code, in this case the subcode of all codewords within a certain ball. This bound is useful for large codes with relatively small minimum distances.
gap> UpperBoundPlotkin( 16, 3, 2 ); 12288 gap> UpperBoundElias( 16, 3, 2 ); 10280
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