The conorm code of an AG-code

Given a suitable extension F′/F of algebraic function fields over a finite field Fq, we introduce the conorm code ConF′/F(C) defined over F′ which is constructed from an algebraic geometry code C defined over F. We study the parameters of ConF′/F(C) in terms of the parameters of C, the ramification...

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Detalhes bibliográficos
Autores: Chara, María de Los Ángeles, Podesta, Ricardo Alberto, Toledano, Ricardo Daniel
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2021
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositório:CONICET Digital (CONICET)
Idioma:inglês
OAI Identifier:oai:ri.conicet.gov.ar:11336/172735
Acesso em linha:http://hdl.handle.net/11336/172735
Access Level:Acceso aberto
Palavra-chave:AG CODES
FINITE FIELDS
FUNCTION FIELDS
CONORM MAP
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling The conorm code of an AG-codeChara, María de Los ÁngelesPodesta, Ricardo AlbertoToledano, Ricardo DanielAG CODESFINITE FIELDSFUNCTION FIELDSCONORM MAPhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given a suitable extension F′/F of algebraic function fields over a finite field Fq, we introduce the conorm code ConF′/F(C) defined over F′ which is constructed from an algebraic geometry code C defined over F. We study the parameters of ConF′/F(C) in terms of the parameters of C, the ramification behavior of the places used to define C and the genus of F. In the case of unramified extensions of function fields we prove that ConF′/F(C)⊥=ConF′/F(C⊥) when the degree of the extension is coprime to the characteristic of Fq. We also study the conorm of cyclic algebraic-geometry codes and we show that some repetition codes, Hermitian codes and all Reed-Solomon codes can be represented as conorm codes.Fil: Chara, María de Los Ángeles. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; ArgentinaFil: Podesta, Ricardo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Toledano, Ricardo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; ArgentinaAmerican Institute of Mathematical Sciences2021-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/172735Chara, María de Los Ángeles; Podesta, Ricardo Alberto; Toledano, Ricardo Daniel; The conorm code of an AG-code; American Institute of Mathematical Sciences; Advances In Mathematics Of Communications; 11-2021; 1-191930-53381930-5346CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.3934/amc.2021018info:eu-repo/semantics/altIdentifier/url/https://www.aimsciences.org/article/doi/10.3934/amc.2021018info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:48:43Zoai:ri.conicet.gov.ar:11336/172735instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982024-05-08 13:48:44.201CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The conorm code of an AG-code
title The conorm code of an AG-code
spellingShingle The conorm code of an AG-code
Chara, María de Los Ángeles
AG CODES
FINITE FIELDS
FUNCTION FIELDS
CONORM MAP
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short The conorm code of an AG-code
title_full The conorm code of an AG-code
title_fullStr The conorm code of an AG-code
title_full_unstemmed The conorm code of an AG-code
title_sort The conorm code of an AG-code
dc.creator.none.fl_str_mv Chara, María de Los Ángeles
Podesta, Ricardo Alberto
Toledano, Ricardo Daniel
author Chara, María de Los Ángeles
author_facet Chara, María de Los Ángeles
Podesta, Ricardo Alberto
Toledano, Ricardo Daniel
author_role author
author2 Podesta, Ricardo Alberto
Toledano, Ricardo Daniel
author2_role author
author
dc.subject.none.fl_str_mv AG CODES
FINITE FIELDS
FUNCTION FIELDS
CONORM MAP
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic AG CODES
FINITE FIELDS
FUNCTION FIELDS
CONORM MAP
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description Given a suitable extension F′/F of algebraic function fields over a finite field Fq, we introduce the conorm code ConF′/F(C) defined over F′ which is constructed from an algebraic geometry code C defined over F. We study the parameters of ConF′/F(C) in terms of the parameters of C, the ramification behavior of the places used to define C and the genus of F. In the case of unramified extensions of function fields we prove that ConF′/F(C)⊥=ConF′/F(C⊥) when the degree of the extension is coprime to the characteristic of Fq. We also study the conorm of cyclic algebraic-geometry codes and we show that some repetition codes, Hermitian codes and all Reed-Solomon codes can be represented as conorm codes.
publishDate 2021
dc.date.none.fl_str_mv 2021-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/172735
Chara, María de Los Ángeles; Podesta, Ricardo Alberto; Toledano, Ricardo Daniel; The conorm code of an AG-code; American Institute of Mathematical Sciences; Advances In Mathematics Of Communications; 11-2021; 1-19
1930-5338
1930-5346
CONICET Digital
CONICET
url http://hdl.handle.net/11336/172735
identifier_str_mv Chara, María de Los Ángeles; Podesta, Ricardo Alberto; Toledano, Ricardo Daniel; The conorm code of an AG-code; American Institute of Mathematical Sciences; Advances In Mathematics Of Communications; 11-2021; 1-19
1930-5338
1930-5346
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.3934/amc.2021018
info:eu-repo/semantics/altIdentifier/url/https://www.aimsciences.org/article/doi/10.3934/amc.2021018
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 15,812429

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