Locally recoverable codes from towers of function fields

Autores
Chara, María de Los Ángeles; Galluccio, Francisco; Martínez Moro, Edgar
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work we construct sequences of locally recoverable AG codes arising from a tower of function fields and give bound for the parameters of the obtained codes. In a particular case of a tower over q2 for any odd q, defined by Garcia and Stichtenoth in [GS2007], we show that the bound is sharp for the first code in the sequence, and we include a detailed analysis for the following codes in the sequence based on the distribution of rational places that split completely in the considered function field extension.
Fil: Chara, María de Los Ángeles. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química. Departamento de Matemáticas; Argentina
Fil: Galluccio, Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química. Departamento de Matemáticas; Argentina
Fil: Martínez Moro, Edgar. Universidad de Valladolid. Instituto de Investigacion En Matematicas.; España
Materia
Function fields
Towers
Codes
LRC
Asymptotic behavior
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/215808
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Locally recoverable codes from towers of function fieldsChara, María de Los ÁngelesGalluccio, FranciscoMartínez Moro, EdgarFunction fieldsTowersCodesLRCAsymptotic behaviorhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this work we construct sequences of locally recoverable AG codes arising from a tower of function fields and give bound for the parameters of the obtained codes. In a particular case of a tower over q2 for any odd q, defined by Garcia and Stichtenoth in [GS2007], we show that the bound is sharp for the first code in the sequence, and we include a detailed analysis for the following codes in the sequence based on the distribution of rational places that split completely in the considered function field extension.Fil: Chara, María de Los Ángeles. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química. Departamento de Matemáticas; ArgentinaFil: Galluccio, Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química. Departamento de Matemáticas; ArgentinaFil: Martínez Moro, Edgar. Universidad de Valladolid. Instituto de Investigacion En Matematicas.; EspañaCornell University2022-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/215808Chara, María de Los Ángeles; Galluccio, Francisco; Martínez Moro, Edgar; Locally recoverable codes from towers of function fields; Cornell University; arXiv; 9-2022; 1-172331-8422CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2209.07136info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2209.07136info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:45:08Zoai:ri.conicet.gov.ar:11336/215808instacron: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:34982025-09-03 09:45:08.99CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Locally recoverable codes from towers of function fields
title Locally recoverable codes from towers of function fields
spellingShingle Locally recoverable codes from towers of function fields
Chara, María de Los Ángeles
Function fields
Towers
Codes
LRC
Asymptotic behavior
title_short Locally recoverable codes from towers of function fields
title_full Locally recoverable codes from towers of function fields
title_fullStr Locally recoverable codes from towers of function fields
title_full_unstemmed Locally recoverable codes from towers of function fields
title_sort Locally recoverable codes from towers of function fields
dc.creator.none.fl_str_mv Chara, María de Los Ángeles
Galluccio, Francisco
Martínez Moro, Edgar
author Chara, María de Los Ángeles
author_facet Chara, María de Los Ángeles
Galluccio, Francisco
Martínez Moro, Edgar
author_role author
author2 Galluccio, Francisco
Martínez Moro, Edgar
author2_role author
author
dc.subject.none.fl_str_mv Function fields
Towers
Codes
LRC
Asymptotic behavior
topic Function fields
Towers
Codes
LRC
Asymptotic behavior
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this work we construct sequences of locally recoverable AG codes arising from a tower of function fields and give bound for the parameters of the obtained codes. In a particular case of a tower over q2 for any odd q, defined by Garcia and Stichtenoth in [GS2007], we show that the bound is sharp for the first code in the sequence, and we include a detailed analysis for the following codes in the sequence based on the distribution of rational places that split completely in the considered function field extension.
Fil: Chara, María de Los Ángeles. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química. Departamento de Matemáticas; Argentina
Fil: Galluccio, Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química. Departamento de Matemáticas; Argentina
Fil: Martínez Moro, Edgar. Universidad de Valladolid. Instituto de Investigacion En Matematicas.; España
description In this work we construct sequences of locally recoverable AG codes arising from a tower of function fields and give bound for the parameters of the obtained codes. In a particular case of a tower over q2 for any odd q, defined by Garcia and Stichtenoth in [GS2007], we show that the bound is sharp for the first code in the sequence, and we include a detailed analysis for the following codes in the sequence based on the distribution of rational places that split completely in the considered function field extension.
publishDate 2022
dc.date.none.fl_str_mv 2022-09
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/11336/215808
Chara, María de Los Ángeles; Galluccio, Francisco; Martínez Moro, Edgar; Locally recoverable codes from towers of function fields; Cornell University; arXiv; 9-2022; 1-17
2331-8422
CONICET Digital
CONICET
url http://hdl.handle.net/11336/215808
identifier_str_mv Chara, María de Los Ángeles; Galluccio, Francisco; Martínez Moro, Edgar; Locally recoverable codes from towers of function fields; Cornell University; arXiv; 9-2022; 1-17
2331-8422
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2209.07136
info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2209.07136
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Cornell University
publisher.none.fl_str_mv Cornell University
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
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
_version_ 1842268712535588864
score 13.13397

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