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IEEE Transactions on Information Theory (2012)
Decoding Cyclic Codes up to a New Bound on the Minimum Distance
Alexander Zeh 1, 2, Antonia Wachter 2, 3, Sergey Bezzateev 4
(01/05/2012)

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 [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
Géométrie algébrique réelle
Informatique/Théorie de l'information

Mathématiques/Théorie de l'information et codage
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