On Upper Bounds for Minimum Distance and Covering Radius of Non-binary Codes |
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Authors: | Tero Laihonen Simon Litsyn |
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Affiliation: | (1) Department of Mathematics, University of Turku, FIN-20500 Turku, Finland.;(2) Department of EE-systems, Tel-Aviv University, Ramat-Aviv, 69978, Israel. |
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Abstract: | We consider upper bounds on two fundamental parameters of a code; minimum distance and covering radius. New upper bounds on the covering radius of non-binary linear codes are derived by generalizing a method due to S. Litsyn and A. Tietäväinen lt:newu and combining it with a new upper bound on the asymptotic information rate of non-binary codes. The upper bound on the information rate is an application of a shortening method of a code and is an analogue of the Shannon-Gallager-Berlekamp straight line bound on error probability. These results improve on the best presently known asymptotic upper bounds on minimum distance and covering radius of non-binary codes in certain intervals. |
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Keywords: | minimum distance covering radius asymptotic information rate dual distance |
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