RT info:eu-repo/semantics/article
T1 Subfield subcodes of projective Reed-Muller codes
A1 Giménez, Philippe Thierry
A1 Ruano Benito, Diego
A1 San José Rubio, Rodrigo
K1 Coding theory
K1 Software engineering
K1 Projective Reed-Muller codes
K1 Linear codes
K1 Subfield subcodes
K1 Códigos proyectivos Reed-Muller
K1 Códigos lineales
K1 Subcódigos de subcampo
K1 12 Matemáticas
K1 1203.17 Informática
AB 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.
PB Elsevier
SN 1071-5797
YR 2024
FD 2024
LK https://uvadoc.uva.es/handle/10324/64636
UL https://uvadoc.uva.es/handle/10324/64636
LA eng
NO Finite Fields and Their Applications, 2024, vol. 94, 102353
NO Producción Científica
DS UVaDOC
RD 22-nov-2024