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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 2024-01-17T09:43:48Z 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 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. eng 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 Subfield subcodes of projective Reed-Muller codes info:eu-repo/semantics/article