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Preprints, Working Papers, ... Year : 2015

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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Dates and versions

hal-01161783 , version 1 (09-06-2015)

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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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