34 research outputs found
A generalization of bounds for cyclic codes, including the HT and BS bounds
We use the algebraic structure of cyclic codes and some properties of the
discrete Fourier transform to give a reformulation of several classical bounds
for the distance of cyclic codes, by extending techniques of linear algebra. We
propose a bound, whose computational complexity is polynomial bounded, which is
a generalization of the Hartmann-Tzeng bound and the Betti-Sala bound. In the
majority of computed cases, our bound is the tightest among all known
polynomial-time bounds, including the Roos bound
Decoding Cyclic Codes up to a New Bound on the Minimum Distance
A new lower bound on the minimum distance of q-ary cyclic codes is proposed.
This bound improves upon the Bose-Chaudhuri-Hocquenghem (BCH) bound and, for
some codes, upon the Hartmann-Tzeng (HT) bound. Several Boston bounds are
special cases of our bound. For some classes of codes the bound on the minimum
distance is refined. Furthermore, a quadratic-time decoding algorithm up to
this new bound is developed. The determination of the error locations is based
on the Euclidean Algorithm and a modified Chien search. The error evaluation is
done by solving a generalization of Forney's formula
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
Describing A Cyclic Code by Another Cyclic Code
A new approach to bound the minimum distance of -ary cyclic codes is
presented. The connection to the BCH and the Hartmann--Tzeng bound is
formulated and it is shown that for several cases an improvement is achieved.
We associate a second cyclic code to the original one and bound its minimum
distance in terms of parameters of the associated code
Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes
Two generalizations of the Hartmann-Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed. The first one is proven by embedding the given cyclic code into a cyclic product code. Furthermore, we show that unique decoding up to this bound is always possible and outline a quadratic-time syndrome-based error decoding algorithm. The second bound is stronger and the proof is more involved. Our technique of embedding the code into a cyclic product code can be applied to other bounds, too and therefore generalizes them
Decoding interleaved Reed-Solomon codes beyond their joint error-correcting capability
International audienceA new probabilistic decoding algorithm for low-rate interleaved Reed-Solomon (IRS) codes is presented. This approach increases the error correcting capability of IRS codes compared to other known approaches (e.g. joint decoding) with high probability. It is a generalization of well-known decoding approaches and its complexity is quadratic with the length of the code. Asymptotic parameters of the new approach are calculated and simulation results are shown to illustrate its performance. Moreover, an upper bound on the failure probability is derived