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.
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Original Russian Text © A. Zeh, M. Ulmschneider, 2015, published in Problemy Peredachi Informatsii, 2015, Vol. 51, No. 3, pp. 15–30.
Supported by the German Research Council (DFG) under grants Bo867/22-1 and Ze1016/1-1; the work was initiated when both authors were affiliated with the Institute of Communications Engineering, University of Ulm, Ulm, Germany.
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Zeh, A., Ulmschneider, M. Decoding of repeated-root cyclic codes up to new bounds on their minimum distance. Probl Inf Transm 51, 217–230 (2015). https://doi.org/10.1134/S0032946015030023
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DOI: https://doi.org/10.1134/S0032946015030023