Subfield subcodes of projective Reed-Muller codes
Producción Científica
| Autores: | , , |
|---|---|
| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Recursos: | Universidad de Valladolid |
| Repositorio: | UVaDOC. Repositorio Documental de la Universidad de Valladolid |
| OAI Identifier: | oai:uvadoc.uva.es:10324/64636 |
| Acesso em linha: | https://doi.org/10.1016/j.ffa.2023.102353 https://uvadoc.uva.es/handle/10324/64636 |
| Access Level: | acceso abierto |
| Palavra-chave: | Coding theory Software engineering Projective Reed-Muller codes Linear codes Subfield subcodes Códigos proyectivos Reed-Muller Códigos lineales Subcódigos de subcampo 12 Matemáticas 1203.17 Informática |
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Subfield subcodes of projective Reed-Muller codesGiménez, Philippe ThierryRuano Benito, DiegoSan José Rubio, RodrigoCoding theorySoftware engineeringProjective Reed-Muller codesLinear codesSubfield subcodesCódigos proyectivos Reed-MullerCódigos linealesSubcódigos de subcampo12 Matemáticas1203.17 InformáticaProducción CientíficaExplicit bases for the subfield subcodes of projective Reed-Muller codes over the projective plane and their duals are obtained. In particular, we provide a formula for the dimension of these codes. For the general case over the projective space, we generalize the necessary tools to deal with this case as well: we obtain a universal Gröbner basis for the vanishing ideal of the set of standard representatives of the projective space and we show how to reduce any monomial with respect to this Gröbner basis. With respect to the parameters of these codes, by considering subfield subcodes of projective Reed-Muller codes we obtain long linear codes with good parameters over a small finite field.Elsevier2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://doi.org/10.1016/j.ffa.2023.102353https://uvadoc.uva.es/handle/10324/64636reponame:UVaDOC. Repositorio Documental de la Universidad de Valladolidinstname:Universidad de ValladolidIngléshttps://www.sciencedirect.com/science/article/pii/S1071579723001958?via%3Dihubinfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/oai:uvadoc.uva.es:10324/646362026-06-13T12:44:47Z |
| dc.title.none.fl_str_mv |
Subfield subcodes of projective Reed-Muller codes |
| title |
Subfield subcodes of projective Reed-Muller codes |
| spellingShingle |
Subfield subcodes of projective Reed-Muller codes Giménez, Philippe Thierry Coding theory Software engineering Projective Reed-Muller codes Linear codes Subfield subcodes Códigos proyectivos Reed-Muller Códigos lineales Subcódigos de subcampo 12 Matemáticas 1203.17 Informática |
| title_short |
Subfield subcodes of projective Reed-Muller codes |
| title_full |
Subfield subcodes of projective Reed-Muller codes |
| title_fullStr |
Subfield subcodes of projective Reed-Muller codes |
| title_full_unstemmed |
Subfield subcodes of projective Reed-Muller codes |
| title_sort |
Subfield subcodes of projective Reed-Muller codes |
| dc.creator.none.fl_str_mv |
Giménez, Philippe Thierry Ruano Benito, Diego San José Rubio, Rodrigo |
| author |
Giménez, Philippe Thierry |
| author_facet |
Giménez, Philippe Thierry Ruano Benito, Diego San José Rubio, Rodrigo |
| author_role |
author |
| author2 |
Ruano Benito, Diego San José Rubio, Rodrigo |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Coding theory Software engineering Projective Reed-Muller codes Linear codes Subfield subcodes Códigos proyectivos Reed-Muller Códigos lineales Subcódigos de subcampo 12 Matemáticas 1203.17 Informática |
| topic |
Coding theory Software engineering Projective Reed-Muller codes Linear codes Subfield subcodes Códigos proyectivos Reed-Muller Códigos lineales Subcódigos de subcampo 12 Matemáticas 1203.17 Informática |
| description |
Producción Científica |
| publishDate |
2024 |
| dc.date.none.fl_str_mv |
2024 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
https://doi.org/10.1016/j.ffa.2023.102353 https://uvadoc.uva.es/handle/10324/64636 |
| url |
https://doi.org/10.1016/j.ffa.2023.102353 https://uvadoc.uva.es/handle/10324/64636 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
https://www.sciencedirect.com/science/article/pii/S1071579723001958?via%3Dihub |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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application/pdf |
| dc.publisher.none.fl_str_mv |
Elsevier |
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Elsevier |
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reponame:UVaDOC. Repositorio Documental de la Universidad de Valladolid instname:Universidad de Valladolid |
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Universidad de Valladolid |
| reponame_str |
UVaDOC. Repositorio Documental de la Universidad de Valladolid |
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UVaDOC. Repositorio Documental de la Universidad de Valladolid |
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1869425333194719232 |
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15,301629 |