Decoding cyclic codes up to a new bound on the minimum distance

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

doi:10.1109/TIT.2012.2185924

Decoding cyclic codes up to a new bound on the minimum distance

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

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

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.

Original language	English
Article number	6144739
Pages (from-to)	3951-3960
Number of pages	10
Journal	IEEE Transactions on Information Theory
Volume	58
Issue number	6
DOIs	https://doi.org/10.1109/TIT.2012.2185924
State	Published - 2012
Externally published	Yes

Keywords

Bose-Chaudhuri-Hocquenghem (BCH) bound
Forney's formula
Hartmann-Tzeng (HT) bound
Roos bound
cyclic codes
decoding

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10.1109/TIT.2012.2185924

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title = "Decoding cyclic codes up to a new bound on the minimum distance",

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 = "Bose-Chaudhuri-Hocquenghem (BCH) bound, Forney's formula, Hartmann-Tzeng (HT) bound, Roos bound, cyclic codes, decoding",

author = "Alexander Zeh and Antonia Wachter-Zeh and Bezzateev, \{Sergey V.\}",

note = "Funding Information: Manuscript received May 08, 2011; revised November 02, 2011; accepted January 15, 2012. Date of publication February 03, 2012; date of current version May 15, 2012. This work was supported by the Deutsche Forschungsgemein-schaft under Grants BO 867/22-1 and BO 867/21-1. The material in this paper was presented in part at the 2011 IEEE International Symposium on Information Theory [1].",

year = "2012",

doi = "10.1109/TIT.2012.2185924",

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AU - Wachter-Zeh, Antonia

AU - Bezzateev, Sergey V.

N1 - Funding Information: Manuscript received May 08, 2011; revised November 02, 2011; accepted January 15, 2012. Date of publication February 03, 2012; date of current version May 15, 2012. This work was supported by the Deutsche Forschungsgemein-schaft under Grants BO 867/22-1 and BO 867/21-1. The material in this paper was presented in part at the 2011 IEEE International Symposium on Information Theory [1].

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Bose-Chaudhuri-Hocquenghem (BCH) bound

KW - Forney's formula

KW - Hartmann-Tzeng (HT) bound

KW - Roos bound

KW - cyclic codes

KW - decoding

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DO - 10.1109/TIT.2012.2185924

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SN - 0018-9448

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EP - 3960

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 6

M1 - 6144739

ER -

Decoding cyclic codes up to a new bound on the minimum distance

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Keywords

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