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| HAL: inria-00607733, version 1 |
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| WCC 2011 - Workshop on coding and cryptography, Paris : France (2011) |
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| Algebraic Decoding of Negacyclic Codes over Z4 |
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| Eimear Byrne 1Marcus Greferath 1 |
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| (2011-04) |
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| We investigate Berlekamp's negacyclic codes and discover that these codes, when considered over the integers modulo 4, do not su er any of the restrictions on the minimum distance observed in Berlekamp's original papers [2, 3]. We present an algebraic decoding algorithm for this class of codes that corrects any error pattern of Lee weight t. Our treatment uses Grobner bases, the decoding complexity is quadratic in t. |
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| 1: | Claude Shannon Institute |
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School of Mathematical Sciences University College Dublin, |
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| 2: | Departament d'Enginyeria de la Informacio i de les Comunicacions |
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Universitat Autonoma de Barcelona, Espa~na? |
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| Domain | : | Computer Science/Cryptography and Security Computer Science/Discrete Mathematics Computer Science/Information Theory and Coding Mathematics/Information Theory |
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| negacyclic code – integers modulo 4 – Lee metric – Galois Ring – decoding – Grobner bases – key equation – solution by approximations – module of solutions. |
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| inria-00607733, version 1 | |
| http://hal.inria.fr/inria-00607733 | |
| oai:hal.inria.fr:inria-00607733 | |
| From: Assia Saadi | |
| Submitted on: Monday, 11 July 2011 10:23:04 | |
| Updated on: Monday, 11 July 2011 10:50:59 | |
