Unidirectional covering codes

A code C/spl sube/Z/sup n//sub 2/, where Z/sub 2/={0,1}, has unidirectional covering radius R if R is the smallest integer so that any word in Z/sup n//sub 2/ can be obtained from at least one codeword c/spl isin/C by replacing either 1s by 0s in at most R coordinates or 0s by 1s in at most R coordi...

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Veröffentlicht in:	IEEE transactions on information theory 2006-01, Vol.52 (1), p.336-340
Hauptverfasser:	Ostergard, P.R.J., Seuranen, E.A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Codes Coding, codes Construction Covering Covering codes Data compression Error correction codes Exact sciences and technology Information theory Information, signal and communications theory Integer programming Linear programming Lower bounds Mathematical models Searching Signal and communications theory Tabu search Telecommunications and information theory unidirectional codes Upper bound Upper bounds
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Beschreibung
Zusammenfassung:	A code C/spl sube/Z/sup n//sub 2/, where Z/sub 2/={0,1}, has unidirectional covering radius R if R is the smallest integer so that any word in Z/sup n//sub 2/ can be obtained from at least one codeword c/spl isin/C by replacing either 1s by 0s in at most R coordinates or 0s by 1s in at most R coordinates. The minimum cardinality of such a code is denoted by E(n,R). Upper bounds on this function are here obtained by constructing codes using tabu search; lower bounds, on the other hand, are mainly obtained by integer programming and exhaustive search. Best known bounds on E(n,R) for n/spl les/13 and R/spl les/6 are tabulated.
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2005.860449