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

Author

Zeh, Alexander ; Wachter-Zeh, Antonia ; Bezzateev, Sergey V.

Author_Institution

Inst. of Commun. Eng., Univ. of Ulm, Ulm, Germany

Volume

58

Issue

6

fYear

2012

fDate

6/1/2012 12:00:00 AM

Firstpage

3951

Lastpage

3960

Abstract

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.

Keywords

cyclic codes; decoding; error detection codes; Bose-Chaudhuri-Hocquenghem bound improvement; Boston bounds; Euclidean algorithm; Forney formula generalization; Hartmann-Tzeng bound improvement; decoding cyclic codes; error evaluation; error location determination; lower bound; minimum distance; modified Chien search; q-ary cyclic code; quadratic-time decoding algorithm; Decoding; Educational institutions; Electronic mail; Generators; Iterative decoding; Polynomials; Bose–Chaudhuri–Hocquenghem (BCH) bound; Forney´s formula; Hartmann–Tzeng (HT) bound; Roos bound; cyclic codes; decoding;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2012.2185924

Filename

6144739