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| HAL : hal-00678646, version 1 |
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| IEEE Transactions on Information Theory (2012) |
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| Decoding Cyclic Codes up to a New Bound on the Minimum Distance |
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| Alexander Zeh 1, 2Antonia Wachter 2, 3 |
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| (01/05/2012) |
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| 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. |
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| 1 : | TANC (INRIA Saclay - Ile de France) |
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INRIA – Polytechnique - X – CNRS : UMR7161 |
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| 2 : | Institute of Communications Engineering [Ulm] (INT - University of Ulm.) |
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University of Ulm |
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| 3 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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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 |
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| 4 : | Saint Petersburg University of Aerospace Instrumentation (SUAI) |
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Saint Petersburg University of Aerospace Instrumentation |
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| Géométrie algébrique réelle |
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| Domaine | : | Informatique/Théorie de l'information et codage Mathématiques/Théorie de l'information et codage |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00678646, version 1 | |
| http://hal.inria.fr/hal-00678646 | |
| oai:hal.inria.fr:hal-00678646 | |
| Contributeur : Alexander Zeh | |
| Soumis le : Mardi 13 Mars 2012, 17:10:19 | |
| Dernière modification le : Mercredi 14 Mars 2012, 09:51:32 | |
