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Problemy Peredachi Informatsii, 1998, Volume 34, Issue 2, Pages 16–31
(Mi ppi400)
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This article is cited in 4 scientific papers (total in 4 papers)
Information Theory and Coding Theory
On Linear Programming Bounds for Codes in Polynomial Metric Spaces
P. Boyvalenkov, D. Danev
Abstract:
We describe a general approach for studying the possibilities for improvements of the best known universal linear programming bounds on the cardinality and the minimum distance of codes in a polynomial metric space $\mathcal M$ (finite or infinite). We introduce functions $P_j(\mathcal M,s)$ having the property that $P_j(\mathcal M,s)<0$ for some $j$ if and only if the universal linear programming bound (1) can be improved by linear programming. A formula for $P_j(\mathcal M,s)$ depending on the zonal spherical functions (corresponding to $\mathcal M$) and $s$ is given. Applications in different polynomial metric spaces are considered with special emphasis on the Euclidean spheres and the binary Hamming space. Methods for obtaining new bounds (when $P_j(\mathcal M,s)<0$ for some $j$) on the size of codes and the code distance are presented. An algorithm for computer calculations of $P_j(\mathcal M,s)$ is described.
Received: 06.09.1996 Revised: 21.04.1997
Citation:
P. Boyvalenkov, D. Danev, “On Linear Programming Bounds for Codes in Polynomial Metric Spaces”, Probl. Peredachi Inf., 34:2 (1998), 16–31; Problems Inform. Transmission, 34:2 (1998), 108–120
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https://www.mathnet.ru/eng/ppi400 https://www.mathnet.ru/eng/ppi/v34/i2/p16
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Abstract page: | 274 | Full-text PDF : | 95 | References: | 35 |
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