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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/194858
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T10:02:20Zoai: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:34982025-09-29 10:02:20.584CONICET 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) |
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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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1844613826365882368 |
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13.070432 |