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Problemy Peredachi Informatsii, 2015, Volume 51, Issue 3, Pages 15–30
(Mi ppi2177)
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This article is cited in 3 scientific papers (total in 3 papers)
Coding Theory
Decoding of repeated-root cyclic codes up to new bounds on their minimum distance
A. Zeha, M. Ulmschneiderb a Computer Science Department, Technion, Haifa, Israel
b Institute of Communications and Navigation, German Aerospace Center (DLR), Berlin, Germany
Abstract:
The well-known approach of Bose, Ray–Chaudhuri, and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum Hamming distance of simple-root cyclic codes. We generalize these two bounds to the case of repeated-root cyclic codes and present a syndrome-based burst error decoding algorithm with guaranteed decoding radius based on an associated folded cyclic code. Furthermore, we present a third technique for bounding the minimum Hamming distance based on the embedding of a given repeated-root cyclic code into a repeated-root cyclic product code. A second quadratic-time probabilistic burst error decoding procedure based on the third bound is outlined.
Received: 22.11.2013 Revised: 24.03.2015
Citation:
A. Zeh, M. Ulmschneider, “Decoding of repeated-root cyclic codes up to new bounds on their minimum distance”, Probl. Peredachi Inf., 51:3 (2015), 15–30; Problems Inform. Transmission, 51:3 (2015), 217–230
Linking options:
https://www.mathnet.ru/eng/ppi2177 https://www.mathnet.ru/eng/ppi/v51/i3/p15
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Abstract page: | 212 | Full-text PDF : | 41 | References: | 73 | First page: | 52 |
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