Singularities of Symmetric Hypersurfaces and Reed-Solomon Codes

Autores
Cafure, Antonio Artemio; Matera, Guillermo; Privitelli, Melina Lorena
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We determine conditions on q for the nonexistence of deep holes of the standard Reed-Solomon code of dimension k over Fq generated by polynomials of degree k + d. Our conditions rely on the existence of q-rational points with nonzero, pairwise-distinct coordinates of a certain family of hypersurfaces defined over Fq. We show that the hypersurfaces under consideration are invariant under the action of the symmetric group of permutations of the coordinates. This allows us to obtain critical information concerning the singular locus of these hypersurfaces, from which the existence of q-rational points is established.
Fil: Cafure, Antonio Artemio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina
Fil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina
Fil: Privitelli, Melina Lorena. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
DEEP HOLES
FINITE FIELDS
RATIONAL POINTS
REED-SOLOMON CODES
SINGULAR HYPERSURFACES
SYMMETRIC POLYNOMIALS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/194858
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/194858
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Singularities of Symmetric Hypersurfaces and Reed-Solomon CodesCafure, Antonio ArtemioMatera, GuillermoPrivitelli, Melina LorenaDEEP HOLESFINITE FIELDSRATIONAL POINTSREED-SOLOMON CODESSINGULAR HYPERSURFACESSYMMETRIC POLYNOMIALShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We determine conditions on q for the nonexistence of deep holes of the standard Reed-Solomon code of dimension k over Fq generated by polynomials of degree k + d. Our conditions rely on the existence of q-rational points with nonzero, pairwise-distinct coordinates of a certain family of hypersurfaces defined over Fq. We show that the hypersurfaces under consideration are invariant under the action of the symmetric group of permutations of the coordinates. This allows us to obtain critical information concerning the singular locus of these hypersurfaces, from which the existence of q-rational points is established.Fil: Cafure, Antonio Artemio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; ArgentinaFil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; ArgentinaFil: Privitelli, Melina Lorena. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Institute of Mathematical Sciences2012-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/194858Cafure, Antonio Artemio; Matera, Guillermo; Privitelli, Melina Lorena; Singularities of Symmetric Hypersurfaces and Reed-Solomon Codes; American Institute of Mathematical Sciences; Advances In Mathematics Of Communications; 6; 1; 2-2012; 69-941930-5346CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.3934/amc.2012.6.69info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:31:47Zoai:ri.conicet.gov.ar:11336/194858instacron: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:34982025-10-22 11:31:47.98CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Singularities of Symmetric Hypersurfaces and Reed-Solomon Codes
title Singularities of Symmetric Hypersurfaces and Reed-Solomon Codes
spellingShingle Singularities of Symmetric Hypersurfaces and Reed-Solomon Codes
Cafure, Antonio Artemio
DEEP HOLES
FINITE FIELDS
RATIONAL POINTS
REED-SOLOMON CODES
SINGULAR HYPERSURFACES
SYMMETRIC POLYNOMIALS
title_short Singularities of Symmetric Hypersurfaces and Reed-Solomon Codes
title_full Singularities of Symmetric Hypersurfaces and Reed-Solomon Codes
title_fullStr Singularities of Symmetric Hypersurfaces and Reed-Solomon Codes
title_full_unstemmed Singularities of Symmetric Hypersurfaces and Reed-Solomon Codes
title_sort Singularities of Symmetric Hypersurfaces and Reed-Solomon Codes
dc.creator.none.fl_str_mv Cafure, Antonio Artemio
Matera, Guillermo
Privitelli, Melina Lorena
author Cafure, Antonio Artemio
author_facet Cafure, Antonio Artemio
Matera, Guillermo
Privitelli, Melina Lorena
author_role author
author2 Matera, Guillermo
Privitelli, Melina Lorena
author2_role author
author
dc.subject.none.fl_str_mv DEEP HOLES
FINITE FIELDS
RATIONAL POINTS
REED-SOLOMON CODES
SINGULAR HYPERSURFACES
SYMMETRIC POLYNOMIALS
topic DEEP HOLES
FINITE FIELDS
RATIONAL POINTS
REED-SOLOMON CODES
SINGULAR HYPERSURFACES
SYMMETRIC POLYNOMIALS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We determine conditions on q for the nonexistence of deep holes of the standard Reed-Solomon code of dimension k over Fq generated by polynomials of degree k + d. Our conditions rely on the existence of q-rational points with nonzero, pairwise-distinct coordinates of a certain family of hypersurfaces defined over Fq. We show that the hypersurfaces under consideration are invariant under the action of the symmetric group of permutations of the coordinates. This allows us to obtain critical information concerning the singular locus of these hypersurfaces, from which the existence of q-rational points is established.
Fil: Cafure, Antonio Artemio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina
Fil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina
Fil: Privitelli, Melina Lorena. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We determine conditions on q for the nonexistence of deep holes of the standard Reed-Solomon code of dimension k over Fq generated by polynomials of degree k + d. Our conditions rely on the existence of q-rational points with nonzero, pairwise-distinct coordinates of a certain family of hypersurfaces defined over Fq. We show that the hypersurfaces under consideration are invariant under the action of the symmetric group of permutations of the coordinates. This allows us to obtain critical information concerning the singular locus of these hypersurfaces, from which the existence of q-rational points is established.
publishDate 2012
dc.date.none.fl_str_mv 2012-02
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/11336/194858
Cafure, Antonio Artemio; Matera, Guillermo; Privitelli, Melina Lorena; Singularities of Symmetric Hypersurfaces and Reed-Solomon Codes; American Institute of Mathematical Sciences; Advances In Mathematics Of Communications; 6; 1; 2-2012; 69-94
1930-5346
CONICET Digital
CONICET
url http://hdl.handle.net/11336/194858
identifier_str_mv Cafure, Antonio Artemio; Matera, Guillermo; Privitelli, Melina Lorena; Singularities of Symmetric Hypersurfaces and Reed-Solomon Codes; American Institute of Mathematical Sciences; Advances In Mathematics Of Communications; 6; 1; 2-2012; 69-94
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.2012.6.69
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
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
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
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score 12.982451

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