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...

ver descrição completa

Detalhes bibliográficos
Autores: Andrade, A.A. [UNESP], Interlando, J.C. [UNESP], Palazzo Jr., R.
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2003
País:Brasil
Recursos:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/22134
Acesso em linha:http://dx.doi.org/10.1590/S0101-82052003000200005
http://hdl.handle.net/11449/22134
Access Level:acceso abierto
Palavra-chave: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
Descrição
Resumo: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.