Alternant and BCH codes over certain rings

Bibliographic Details
Main Author: Andrade, A.A. [UNESP]
Publication Date: 2003
Other Authors: Interlando, J.C. [UNESP], Palazzo Jr., R.
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.1590/S0101-82052003000200005
http://hdl.handle.net/11449/22134
Summary: 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 codeBCH 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.Unesp Ibilce Department of MathematicsUnicamp Feec Department of TelematicsUnesp Ibilce Department of MathematicsSociedade Brasileira de Matemática Aplicada e ComputacionalUniversidade Estadual Paulista (Unesp)Universidade Estadual de Campinas (UNICAMP)Andrade, A.A. [UNESP]Interlando, J.C. [UNESP]Palazzo Jr., R.2014-05-20T14:02:50Z2014-05-20T14:02:50Z2003-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article233-247application/pdfhttp://dx.doi.org/10.1590/S0101-82052003000200005Computational & Applied Mathematics. Sociedade Brasileira de Matemática Aplicada e Computacional, v. 22, n. 2, p. 233-247, 2003.1807-0302http://hdl.handle.net/11449/2213410.1590/S0101-82052003000200005S1807-03022003000200005S1807-03022003000200005.pdf8940498347481982SciELOreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengComputational & Applied Mathematicsinfo:eu-repo/semantics/openAccess2024-11-01T14:26:55Zoai:repositorio.unesp.br:11449/22134Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-03-28T14:24:39.888567Repositório 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 code
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 Jr., R.
author_role author
author2 Interlando, J.C. [UNESP]
Palazzo Jr., 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 Jr., R.
dc.subject.por.fl_str_mv 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
topic 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
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
2014-05-20T14:02:50Z
2014-05-20T14:02:50Z
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://dx.doi.org/10.1590/S0101-82052003000200005
Computational & Applied Mathematics. Sociedade Brasileira de Matemática Aplicada e Computacional, v. 22, n. 2, p. 233-247, 2003.
1807-0302
http://hdl.handle.net/11449/22134
10.1590/S0101-82052003000200005
S1807-03022003000200005
S1807-03022003000200005.pdf
8940498347481982
url http://dx.doi.org/10.1590/S0101-82052003000200005
http://hdl.handle.net/11449/22134
identifier_str_mv Computational & Applied Mathematics. Sociedade Brasileira de Matemática Aplicada e Computacional, v. 22, n. 2, p. 233-247, 2003.
1807-0302
10.1590/S0101-82052003000200005
S1807-03022003000200005
S1807-03022003000200005.pdf
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 233-247
application/pdf
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 SciELO
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
_version_ 1834483020797575168

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