Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance

Abstract : The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum 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. Index Terms Bound on the minimum distance, burst error, efficient decoding, folded code, repeated-root cyclic code, repeated-root cyclic product code
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https://hal.inria.fr/hal-01161783
Contributeur : Alexander Zeh <>
Soumis le : mardi 9 juin 2015 - 10:21:30
Dernière modification le : dimanche 31 décembre 2017 - 09:44:02
Document(s) archivé(s) le : mardi 15 septembre 2015 - 13:20:53

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  • HAL Id : hal-01161783, version 1
  • ARXIV : 1506.02820

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Alexander Zeh, Markus Ulmschneider. Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance. 2015. 〈hal-01161783〉

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