Goppa codes over certain semigroups

Bibliographic Details
Main Author: Andrade, Antonio Aparecido de [UNESP]
Publication Date: 2014
Other Authors: Shah, Tariq, Azam, Naveed Ahmed, Hussain, Syed Azmat
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://www.diogenes.bg/ijam/contents/2014-27-1/7/
http://hdl.handle.net/11449/122689
Summary: A Goppa code is described in terms of a polynomial, known as Goppa polynomial, and in contrast to cyclic codes, where it is difficult to estimate the minimum Hamming distance d from the generator polynomial. Furthermore, a Goppa code has the property that d ≥ deg(h(X))+1, where h(X) is a Goppa polynomial. In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm.
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spelling Goppa codes over certain semigroupsGoppa codeSemigroup ringA Goppa code is described in terms of a polynomial, known as Goppa polynomial, and in contrast to cyclic codes, where it is difficult to estimate the minimum Hamming distance d from the generator polynomial. Furthermore, a Goppa code has the property that d ≥ deg(h(X))+1, where h(X) is a Goppa polynomial. In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm.Universidade Estadual Paulista Júlio de Mesquita Filho, Instituto de Biociencias, Letras e Ciencias Exatas de Sao Jose do Rio Preto, Sao Jose do Rio Preto, RUA CRISTOVAO COLOMBO 2265 - DEPARTAMENTO DE MATEMATICA, JARDIM NAZARETH, CEP 15054-000, SP, BrasilUniversidade Estadual Paulista Júlio de Mesquita Filho, Instituto de Biociencias, Letras e Ciencias Exatas de Sao Jose do Rio Preto, Sao Jose do Rio Preto, RUA CRISTOVAO COLOMBO 2265 - DEPARTAMENTO DE MATEMATICA, JARDIM NAZARETH, CEP 15054-000, SP, BrasilDepartment of Mathematics Quaid-i-Azam University Islamabad, PAKISTANFaculty of Engineering Sciences Ghulam Ishaq Khan Institute of Engineering Science and Technology Topi Swabi, PAKISTANSchool of Engineering and Applied Sciences (SEAS) ISRA University Islamabad Campus, PAKISTANUniversidade Estadual Paulista (Unesp)Andrade, Antonio Aparecido de [UNESP]Shah, TariqAzam, Naveed AhmedHussain, Syed Azmat2015-04-27T11:55:57Z2015-04-27T11:55:57Z2014info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article65-71http://www.diogenes.bg/ijam/contents/2014-27-1/7/International Journal of Applied Mathematics, v. 27, n. 1, p. 65-71, 2014.1311-1728http://hdl.handle.net/11449/12268910.12732/ijam.v27i1.78940498347481982Currículo Lattesreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal of Applied Mathematicsinfo:eu-repo/semantics/openAccess2024-11-01T14:27:11Zoai:repositorio.unesp.br:11449/122689Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462024-11-01T14:27:11Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Goppa codes over certain semigroups
title Goppa codes over certain semigroups
spellingShingle Goppa codes over certain semigroups
Andrade, Antonio Aparecido de [UNESP]
Goppa code
Semigroup ring
title_short Goppa codes over certain semigroups
title_full Goppa codes over certain semigroups
title_fullStr Goppa codes over certain semigroups
title_full_unstemmed Goppa codes over certain semigroups
title_sort Goppa codes over certain semigroups
author Andrade, Antonio Aparecido de [UNESP]
author_facet Andrade, Antonio Aparecido de [UNESP]
Shah, Tariq
Azam, Naveed Ahmed
Hussain, Syed Azmat
author_role author
author2 Shah, Tariq
Azam, Naveed Ahmed
Hussain, Syed Azmat
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Andrade, Antonio Aparecido de [UNESP]
Shah, Tariq
Azam, Naveed Ahmed
Hussain, Syed Azmat
dc.subject.por.fl_str_mv Goppa code
Semigroup ring
topic Goppa code
Semigroup ring
description A Goppa code is described in terms of a polynomial, known as Goppa polynomial, and in contrast to cyclic codes, where it is difficult to estimate the minimum Hamming distance d from the generator polynomial. Furthermore, a Goppa code has the property that d ≥ deg(h(X))+1, where h(X) is a Goppa polynomial. In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm.
publishDate 2014
dc.date.none.fl_str_mv 2014
2015-04-27T11:55:57Z
2015-04-27T11:55:57Z
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://www.diogenes.bg/ijam/contents/2014-27-1/7/
International Journal of Applied Mathematics, v. 27, n. 1, p. 65-71, 2014.
1311-1728
http://hdl.handle.net/11449/122689
10.12732/ijam.v27i1.7
8940498347481982
url http://www.diogenes.bg/ijam/contents/2014-27-1/7/
http://hdl.handle.net/11449/122689
identifier_str_mv International Journal of Applied Mathematics, v. 27, n. 1, p. 65-71, 2014.
1311-1728
10.12732/ijam.v27i1.7
8940498347481982
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv International Journal of Applied Mathematics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 65-71
dc.source.none.fl_str_mv Currículo Lattes
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_ 1834483380415102976

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