2015/06/09 by Alexander Zeh, Zeh, Alexander, Markus Ulmschneider +1
Computer Science · Mathematics · #Combinatorics (math.CO) #Cryptography and Security (cs.CR) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #cs.CR #cs.DM #cs.IT #math.CO #math.IT #math.NT
paper · pdf · doi:10.48550/arxiv.1506.02820
arxiv created 2015/06/09 · arxiv updated 2015/06/10
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