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

Giménez, Philippe Thierry Ruano Benito, Diego San José Rubio, Rodrigo 2024 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 https://uvadoc.uva.es/handle/10324/64636 eng Elsevier Coding theory Software engineering 12 Matemáticas 1203.17 Informática Subfield subcodes of projective Reed-Muller codes info:eu-repo/semantics/article TEXT UVaDOC. Repositorio Documental de la Universidad de Valladolid Hispana