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Bounds for binary codes with narrow distance distributions
Roth, Ron M.; Seroussi, Gadiel
HPL-2006-136
Keyword(s): constant-weight codes; distance distribution; equidistant codes; linear programming bound
Abstract: New lower bounds are presented on the second moment of the distance distribution of binary codes, in terms of the first moment of the distribution. These bounds are used to obtain upper bounds on the size of codes whose maximum distance is close to their minimum distance. It is then demonstrated how such bounds can be applied to bound from below the smallest attainable ratio between the maximum distance and the minimum distance of codes. Finally, counterparts of the bounds are derived for the special case of constant-weight codes. Notes:
19 Pages
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