Alternant and BCH codes over certain rings

Detalhes bibliográficos
Autor(a) principal: Andrade, A. A. [UNESP]
Data de Publicação: 2003
Outros Autores: Interlando, J. C. [UNESP], Palazzo, R.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://hdl.handle.net/11449/195753
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 Z(m) 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 Z(m) under Lee metric.UNESP, Dept Math, Ibilce, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilUniv Estadual Campinas, Dept Telemat, Feec, BR-13081970 Campinas, SP, BrazilUNESP, Dept Math, Ibilce, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilSpringerUniversidade Estadual Paulista (Unesp)Universidade Estadual de Campinas (UNICAMP)Andrade, A. A. [UNESP]Interlando, J. C. [UNESP]Palazzo, R.2020-12-10T18:02:22Z2020-12-10T18:02:22Z2003-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article233-247Computational & Applied Mathematics. Heidelberg: Springer Heidelberg, v. 22, n. 2, p. 233-247, 2003.2238-3603http://hdl.handle.net/11449/195753WOS:000208134800005Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengComputational & Applied Mathematicsinfo:eu-repo/semantics/openAccess2021-10-23T11:51:31Zoai:repositorio.unesp.br:11449/195753Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T14:38:53.371031Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)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. [UNESP]
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. [UNESP]
author_facet Andrade, A. A. [UNESP]
Interlando, J. C. [UNESP]
Palazzo, R.
author_role author
author2 Interlando, J. C. [UNESP]
Palazzo, R.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Universidade Estadual de Campinas (UNICAMP)
dc.contributor.author.fl_str_mv Andrade, A. A. [UNESP]
Interlando, J. C. [UNESP]
Palazzo, 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 Z(m) under Lee metric.
publishDate 2003
dc.date.none.fl_str_mv 2003-01-01
2020-12-10T18:02:22Z
2020-12-10T18:02:22Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv Computational & Applied Mathematics. Heidelberg: Springer Heidelberg, v. 22, n. 2, p. 233-247, 2003.
2238-3603
http://hdl.handle.net/11449/195753
WOS:000208134800005
identifier_str_mv Computational & Applied Mathematics. Heidelberg: Springer Heidelberg, v. 22, n. 2, p. 233-247, 2003.
2238-3603
WOS:000208134800005
url http://hdl.handle.net/11449/195753
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Computational & Applied Mathematics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 233-247
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv Web of Science
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808128394697637888

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