3 research outputs found
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
Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes
Cyclic, negacyclic and constacyclic codes are part of a larger class of codes
called polycyclic codes; namely, those codes which can be viewed as ideals of a
factor ring of a polynomial ring. The structure of the ambient ring of
polycyclic codes over GR(p^a,m) and generating sets for its ideals are
considered. Along with some structure details of the ambient ring, the
existance of a certain type of generating set for an ideal is proven.Comment: arXiv admin note: text overlap with arXiv:0906.400