2026-04-14T00:38:45Zhttps://uvadoc.uva.es/oai/request

oai:uvadoc.uva.es:10324/646362024-01-17T20:02:18Zcom_10324_32197com_10324_952com_10324_894col_10324_32199

Giménez, Philippe Thierry ed518ae9f4f06488 600 0000-0002-5436-9837 Ruano Benito, Diego 721b449b68d900c9 600 0000-0001-7304-0087 San José Rubio, Rodrigo 51dd98efaa61c495 500 0000-0002-0944-7584 2024-01-17T09:43:48Z 2024-01-17T09:43:48Z 2024 Finite Fields and Their Applications, 2024, vol. 94, 102353 1071-5797 https://uvadoc.uva.es/handle/10324/64636 10.1016/j.ffa.2023.102353 102353 Finite Fields and Their Applications 94 Producción Científica Explicit 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. application/pdf eng Elsevier info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ © 2023 The Authors Attribution-NonCommercial-NoDerivatives 4.0 Internacional 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 Subfield subcodes of projective Reed-Muller codes info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion https://www.sciencedirect.com/science/article/pii/S1071579723001958?via%3Dihub SI THUMBNAIL Subfield-subcodes-of-projective.pdf.jpg Subfield-subcodes-of-projective.pdf.jpg IM Thumbnail image/jpeg 1989 https://uvadoc.uva.es/bitstream/10324/64636/4/Subfield-subcodes-of-projective.pdf.jpg 673de2380e5bcbd433cb977e4a1f6862 MD5 4 LICENSE license.txt license.txt text/plain 3929 https://uvadoc.uva.es/bitstream/10324/64636/3/license.txt 289d98c1665ee0d20312360f0e8643c8 MD5 3 CC-LICENSE license_rdf license_rdf application/rdf+xml; charset=utf-8 817 https://uvadoc.uva.es/bitstream/10324/64636/2/license_rdf 975848b171c53b753f7e445c8b5bc0e1 MD5 2 ORIGINAL Subfield-subcodes-of-projective.pdf Subfield-subcodes-of-projective.pdf application/pdf 794746 https://uvadoc.uva.es/bitstream/10324/64636/1/Subfield-subcodes-of-projective.pdf ddd0e827e1000ba0abff3f32db2d6d63 MD5 1 10324/64636 oai:uvadoc.uva.es:10324/64636 2024-01-17 21:02:18.949 UVaDOC repositorio@uva.es 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