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

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 cod

A Note on Repeated-Root Cyclic Codes

In papers by Castagnoli et al. and Van Lint, cyclic codes with repeated roots are analyzed. Both papers fail to acknowledge a previous work by Chen, dating back to 1969, which includes an analysis of even, length binary cyclic codes. Results from Chen’s study are presented

Repeated-root cyclic and negacyclic codes over a finite chain ring

AbstractWe show that repeated-root cyclic codes over a finite chain ring are in general not principally generated. Repeated-root negacyclic codes are principally generated if the ring is a Galois ring with characteristic a power of 2. For any other finite chain ring they are in general not principally generated. We also prove results on the structure, cardinality and Hamming distance of repeated-root cyclic and negacyclic codes over a finite chain ring

Repeated-root cyclic and negacyclic codes over a finite chain ring

AbstractWe show that repeated-root cyclic codes over a finite chain ring are in general not principally generated. Repeated-root negacyclic codes are principally generated if the ring is a Galois ring with characteristic a power of 2. For any other finite chain ring they are in general not principally generated. We also prove results on the structure, cardinality and Hamming distance of repeated-root cyclic and negacyclic codes over a finite chain ring

Repeated-root cyclic and negacyclic codes over a finite chain ring

We show that repeated-root cyclic codes over a finite chain ring are in general not principally generated. Repeated-root negacyclic codes are principally generated if the ring is a Galois ring with characteristic a power of 2. For any other finite chain ring they are in general not principally generated. We also prove results on the structure, cardinality and Hamming distance of repeated-root cyclic and negacyclic codes over a finite chain ring

Extending Construction X for Quantum Error-Correcting Codes

In this paper we extend the work of Lisonek and Singh on construction X for quantum error-correcting codes to finite fields of order $p^2^ where p is prime. The results obtained are applied to the dual of Hermitian repeated root cyclic codes to generate new quantum error-correcting codes