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Upper Bound on List-Decoding Radius of Binary Codes.
- Source :
-
IEEE Transactions on Information Theory . Mar2016, Vol. 62 Issue 3, p1119-1128. 10p. - Publication Year :
- 2016
-
Abstract
- Consider the problem of packing Hamming balls of a given relative radius subject to the constraint that they cover any point of the ambient Hamming space with multiplicity at most $L$ . For odd $L\ge 3$ , an asymptotic upper bound on the rate of any such packing is proved. The resulting bound improves the best known bound (due to Blinovsky’1986) for rates below a certain threshold. The method is a superposition of the linear-programming idea of Ashikhmin, Barg, and Litsyn (that was previously used to improve the estimates of Blinovsky for $L=2$ ) and a Ramsey-theoretic technique of Blinovsky. As an application, it is shown that for all odd $L$ , the slope of the rate-radius tradeoff is zero at zero rate. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 62
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 113114899
- Full Text :
- https://doi.org/10.1109/TIT.2016.2516560