Decoding Cyclic Codes up to a New Bound on the Minimum Distance

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 bound and, for some codes, upon the Hartmann-Tzeng bound. Several Boston bounds are special cases of our bound. For some classes of codes, the bound on the minimum di...

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Bibliographic Details
Published in:IEEE transactions on information theory 2012-06, Vol.58 (6), p.3951-3960
Main Authors: Zeh, Alexander, Wachter-Zeh, Antonia, Bezzateev, Sergey V.
Format: Article
Language:eng
Subjects:
Algorithms
Bose-Chaudhuri-Hocquenghem (BCH) bound
Codes
cyclic codes
Decoding
Educational institutions
Electronic mail
Errors
Euclidean space
Forney's formula
Generators
Hartmann-Tzeng (HT) bound
Information theory
Iterative decoding
Lower bounds
Polynomials
Roos bound
Searching
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Summary:A new lower bound on the minimum distance of q -ary cyclic codes is proposed. This bound improves upon the Bose-Chaudhuri-Hocquenghem bound and, for some codes, upon the Hartmann-Tzeng 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.
ISSN:0018-9448
1557-9654