Alternant and BCH codes over certain rings
Alternant codes over arbitrary finite commutative local rings with identity are constructed in terms of parity-check matrices. The derivation is based on the factorization of x s - 1 over the unit group of an appropriate extension of the finite ring. An efficient decoding procedure which makes use o...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2003 |
| País: | Brasil |
| Institución: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unesp.br:11449/22134 |
| Acceso en línea: | http://dx.doi.org/10.1590/S0101-82052003000200005 http://hdl.handle.net/11449/22134 |
| Access Level: | acceso abierto |
| Palabra clave: | codes over rings Alternant code BCH codes Galois extensions of local commutative rings algebraic decoding modified Berlekamp-Massey algorithm errors and erasures decoding Lee metric |
| Sumario: | Alternant codes over arbitrary finite commutative local rings with identity are constructed in terms of parity-check matrices. The derivation is based on the factorization of x s - 1 over the unit group of an appropriate extension of the finite ring. An efficient decoding procedure which makes use of the modified Berlekamp-Massey algorithm to correct errors and erasures is presented. Furthermore, we address the construction of BCH codes over Zm under Lee metric. |
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