Bounds for binary codes with narrow distance distributions

Roth, Ron M. ; Seroussi, Gadiel

HP Development Company

关键词: constant-weight codes;    distance distribution;    equidistant codes;    linear programming bound;   

RP-ID  :  HPL-2006-136

学科分类：计算机科学（综合）

美国|英语

来源: HP Labs

【 摘 要 】

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