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Generalizing bounds on the minimum distance of cyclic codes using cyclic product codes.

Zeh, Alexander and Wachter-Zeh, Antonia and Gadouleau, Maximilien and Bezzateev, Sergey (2013) 'Generalizing bounds on the minimum distance of cyclic codes using cyclic product codes.', in International Symposium on Information Theory Proceedings (ISIT 2013), 7-12 July 2013, Istanbul, Turkey ; proceedings. New York, USA: IEEE, pp. 126-130. IEEE International Symposium on Information Theory.

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.

Item Type:Book chapter
Additional Information:
Keywords:Bound on the minimum distance, Cyclic code, Cyclic product Code, Efficient decoding
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1109/ISIT.2013.6620201
Publisher statement:© 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Date accepted:No date available
Date deposited:28 October 2015
Date of first online publication:2013
Date first made open access:No date available

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