Refinements of Levenshtein Bounds in q-ary Hamming Spaces
We develop refinements of the Levenshtein bound in q-ary Hamming spaces by taking
into account the discrete nature of the distances versus the continuous behavior of
certain parameters used by Levenshtein. We investigate the first relevant cases and
present new bounds. In particular, we derive generalizations and q-ary analogs of
the MacEliece bound. Furthermore, we provide evidence that our approach is as good
as the complete linear programming and discuss how faster are our calculations.
Finally, we present a table with parameters of codes which, if exist, would attain
our bounds.