Alternant and BCH codes over certain rings

Detalhes bibliográficos
Autor(a) principal: Andrade,A.A.
Data de Publicação: 2003
Outros Autores: Interlando,J.C., Palazzo Jr.,R.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000200005
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.
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spelling Alternant and BCH codes over certain ringscodes over ringsalternant codesBCH codesGalois extensions of local commutative ringsalgebraic decodingmodified Berlekamp-Massey algorithmerrors and erasures decodingLee metricAlternant 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.Sociedade Brasileira de Matemática Aplicada e Computacional2003-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000200005Computational & Applied Mathematics v.22 n.2 2003reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S0101-82052003000200005info:eu-repo/semantics/openAccessAndrade,A.A.Interlando,J.C.Palazzo Jr.,R.eng2004-07-19T00:00:00Zoai:scielo:S1807-03022003000200005Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2004-07-19T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv Alternant and BCH codes over certain rings
title Alternant and BCH codes over certain rings
spellingShingle Alternant and BCH codes over certain rings
Andrade,A.A.
codes over rings
alternant codes
BCH codes
Galois extensions of local commutative rings
algebraic decoding
modified Berlekamp-Massey algorithm
errors and erasures decoding
Lee metric
title_short Alternant and BCH codes over certain rings
title_full Alternant and BCH codes over certain rings
title_fullStr Alternant and BCH codes over certain rings
title_full_unstemmed Alternant and BCH codes over certain rings
title_sort Alternant and BCH codes over certain rings
author Andrade,A.A.
author_facet Andrade,A.A.
Interlando,J.C.
Palazzo Jr.,R.
author_role author
author2 Interlando,J.C.
Palazzo Jr.,R.
author2_role author
author
dc.contributor.author.fl_str_mv Andrade,A.A.
Interlando,J.C.
Palazzo Jr.,R.
dc.subject.por.fl_str_mv codes over rings
alternant codes
BCH codes
Galois extensions of local commutative rings
algebraic decoding
modified Berlekamp-Massey algorithm
errors and erasures decoding
Lee metric
topic codes over rings
alternant codes
BCH codes
Galois extensions of local commutative rings
algebraic decoding
modified Berlekamp-Massey algorithm
errors and erasures decoding
Lee metric
description 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.
publishDate 2003
dc.date.none.fl_str_mv 2003-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000200005
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000200005
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0101-82052003000200005
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv Computational & Applied Mathematics v.22 n.2 2003
reponame:Computational & Applied Mathematics
instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron_str SBMAC
institution SBMAC
reponame_str Computational & Applied Mathematics
collection Computational & Applied Mathematics
repository.name.fl_str_mv Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
repository.mail.fl_str_mv ||sbmac@sbmac.org.br
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