Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes

Abstract : Two generalizations of the Hartmann--Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed. The first one is proven by embedding the given cyclic code into a cyclic product code. Furthermore, we show that unique decoding up to this bound is always possible and outline a quadratic-time syndrome-based error decoding algorithm. The second bound is stronger and the proof is more involved. Our technique of embedding the code into a cyclic product code can be applied to other bounds, too and therefore generalizes them.
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Communication dans un congrès
Amos Lapidoth and Igal Sason and Jossy Sayir and Emre Telatar. IEEE International Symposium on Information Theory (ISIT), Jul 2013, Istanbul, Turkey. IEEE, pp.1-6, 2013
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https://hal.inria.fr/hal-00828083
Contributeur : Alexander Zeh <>
Soumis le : mercredi 26 juin 2013 - 14:45:16
Dernière modification le : jeudi 15 novembre 2018 - 11:56:24

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  • HAL Id : hal-00828083, version 1
  • ARXIV : 1301.6231

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Alexander Zeh, Antonia Wachter-Zeh, Maximilien Gadouleau, Sergey Bezzateev. Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes. Amos Lapidoth and Igal Sason and Jossy Sayir and Emre Telatar. IEEE International Symposium on Information Theory (ISIT), Jul 2013, Istanbul, Turkey. IEEE, pp.1-6, 2013. 〈hal-00828083〉

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