Bounds for Binary Codes With Narrow Distance Distributions

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...

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Veröffentlicht in:	IEEE transactions on information theory 2007-08, Vol.53 (8), p.2760-2768
Hauptverfasser:	Roth, R.M., Seroussi, G.
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Australia Binary codes Binary system Cities and towns Codes Coding, codes Computer science Constant-weight codes Data transmission distance distribution equidistant codes Exact sciences and technology Grey-Rankin bound Hamming distance Information theory Information, signal and communications theory Laboratories Linear programming linear programming bound Lower bounds Materials science and technology quasi-symmetric designs self-complementary codes Signal and communications theory Telecommunications and information theory Upper bound Upper bounds
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Beschreibung
Zusammenfassung:	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.
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2007.901192