Hamming and Reed-Solomon codes over certain rings

In this work we present extensions of constructions of Hamming and Reed-Solomon codes over local finite commutative rings with identity obtained from algebraic integer rings of a number field. Also, we present efficient decoding procedures for these codes. The decoding procedure of Reed-Solomon code...

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Detalhes bibliográficos
Autores: Andrade, A. A. [UNESP], Palazzo, R.
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2001
País:Brasil
Recursos:Universidade Estadual Paulista (UNESP)
Repositório:Repositório Institucional da UNESP
Idioma:inglês
OAI Identifier:oai:repositorio.unesp.br:11449/33690
Acesso em linha:http://books.google.com.br/books?id=HkcEzM3QN9IC&lpg=PA265&hl=pt-BR&pg=PA265#v=onepage&q&f=false
http://hdl.handle.net/11449/33690
Access Level:Acceso aberto
Palavra-chave:Hamming code
Reed-Solomon code
modified Berlekamp-Massey algorithm
syndrome calculation
error-location number
Forney's method
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oai_identifier_str oai:repositorio.unesp.br:11449/33690
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spelling Hamming and Reed-Solomon codes over certain ringsHamming codeReed-Solomon codemodified Berlekamp-Massey algorithmsyndrome calculationerror-location numberForney's methodIn this work we present extensions of constructions of Hamming and Reed-Solomon codes over local finite commutative rings with identity obtained from algebraic integer rings of a number field. Also, we present efficient decoding procedures for these codes. The decoding procedure of Reed-Solomon codes is based on the modified Berlekamp-Massey algorithm.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)UNESP, IBMCE, Dept Math, BR-15054000 Sao Jose do Rio Preto, SP, BrazilUniv Estadual Campinas, FEEC, Dept Telemat, BR-13081970 Campinas, SP, BrazilUNESP, IBMCE, Dept Math, BR-15054000 Sao Jose do Rio Preto, SP, BrazilFAPESP: 95/4720-8SpringerUniversidade Estadual Paulista (Unesp)Universidade Estadual de Campinas (UNICAMP)2014-05-20T15:22:46Z2014-05-20T15:22:46Z2001-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article289-306http://books.google.com.br/books?id=HkcEzM3QN9IC&lpg=PA265&hl=pt-BR&pg=PA265#v=onepage&q&f=falseComputational & Applied Mathematics. Heidelberg: Springer Heidelberg, v. 20, n. 3, p. 289-306, 2001.1807-0302http://hdl.handle.net/11449/33690WOS:0002087664000028940498347481982Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengComputational & Applied Mathematicsinfo:eu-repo/semantics/openAccessAndrade, A. A. [UNESP]Palazzo, R.2024-11-01T14:26:58Zoai:repositorio.unesp.br:11449/33690Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462024-11-01T14:26:58Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Hamming and Reed-Solomon codes over certain rings
title Hamming and Reed-Solomon codes over certain rings
spellingShingle Hamming and Reed-Solomon codes over certain rings
Andrade, A. A. [UNESP]
Hamming code
Reed-Solomon code
modified Berlekamp-Massey algorithm
syndrome calculation
error-location number
Forney's method
title_short Hamming and Reed-Solomon codes over certain rings
title_full Hamming and Reed-Solomon codes over certain rings
title_fullStr Hamming and Reed-Solomon codes over certain rings
title_full_unstemmed Hamming and Reed-Solomon codes over certain rings
title_sort Hamming and Reed-Solomon codes over certain rings
dc.creator.none.fl_str_mv Andrade, A. A. [UNESP]
Palazzo, R.
author Andrade, A. A. [UNESP]
author_facet Andrade, A. A. [UNESP]
Palazzo, R.
author_role author
author2 Palazzo, R.
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Universidade Estadual de Campinas (UNICAMP)
dc.subject.por.fl_str_mv Hamming code
Reed-Solomon code
modified Berlekamp-Massey algorithm
syndrome calculation
error-location number
Forney's method
topic Hamming code
Reed-Solomon code
modified Berlekamp-Massey algorithm
syndrome calculation
error-location number
Forney's method
description In this work we present extensions of constructions of Hamming and Reed-Solomon codes over local finite commutative rings with identity obtained from algebraic integer rings of a number field. Also, we present efficient decoding procedures for these codes. The decoding procedure of Reed-Solomon codes is based on the modified Berlekamp-Massey algorithm.
publishDate 2001
dc.date.none.fl_str_mv 2001-01-01
2014-05-20T15:22:46Z
2014-05-20T15:22:46Z
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 http://books.google.com.br/books?id=HkcEzM3QN9IC&lpg=PA265&hl=pt-BR&pg=PA265#v=onepage&q&f=false
Computational & Applied Mathematics. Heidelberg: Springer Heidelberg, v. 20, n. 3, p. 289-306, 2001.
1807-0302
http://hdl.handle.net/11449/33690
WOS:000208766400002
8940498347481982
url http://books.google.com.br/books?id=HkcEzM3QN9IC&lpg=PA265&hl=pt-BR&pg=PA265#v=onepage&q&f=false
http://hdl.handle.net/11449/33690
identifier_str_mv Computational & Applied Mathematics. Heidelberg: Springer Heidelberg, v. 20, n. 3, p. 289-306, 2001.
1807-0302
WOS:000208766400002
8940498347481982
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 289-306
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 repositoriounesp@unesp.br
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score 15,301629

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