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JOURNALS // Problemy Peredachi Informatsii // Archive

Probl. Peredachi Inf., 2015 Volume 51, Issue 3, Pages 15–30 (Mi ppi2177)

This article is cited 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.

UDC: 621.391.15

Received: 22.11.2013
Revised: 24.03.2015


 English version:
Problems of Information Transmission, 2015, 51:3, 217–230

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