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

Alexander Zeh; Antonia Wachter; Sergey Bezzateev

hal-00678646, version 1

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

Alexander Zeh () ^1, 2, Antonia Wachter ^2, 3, Sergey Bezzateev ⁴

IEEE Transactions on Information Theory (2012)

Abstract: 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.

1: TANC (INRIA Saclay - Ile de France)
INRIA – Polytechnique - X – CNRS : UMR7161
2: Institute of Communications Engineering [Ulm] (INT - University of Ulm.)
University of Ulm
3: Institut de Recherche Mathématique de Rennes (IRMAR)
CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne
4: Saint Petersburg University of Aerospace Instrumentation (SUAI)
Saint Petersburg University of Aerospace Instrumentation

hal-00678646, version 1
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From: Alexander Zeh <>
Submitted on: Tuesday, 13 March 2012 17:10:19
Updated on: Wednesday, 14 March 2012 09:51:32

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