RT info:eu-repo/semantics/article
T1 Free resolutions and generalized Hamming weights of binary linear codes
A1 García Marco, Ignacio
A1 Márquez Corbella, Irene
A1 Martínez Moro, Edgar
A1 Pitones, Yuriko
K1 Algebraic geometry
K1 Free resolution
K1 Computer science
K1 Mathematics
K1 Códificación (Informática)
K1 Computer systems
K1 Generalized Hamming weight
K1 Pesos Hamming generalizados
K1 1201.01 Geometría Algebraica
K1 1203.17 Informática
K1 12 Matemáticas
AB In this work, we explore the relationship between the graded free resolution of some monomial ideals and the Generalized Hamming Weights (GHWs) of binary codes. More precisely, we look for a structure that is smaller than the set of codewords of minimal support that provides us with some information about the GHWs. We prove that the first and second generalized Hamming weights of a binary linear code can be computed (by means of a graded free resolution) from a set of monomials associated with a binomial ideal related with the code. Moreover, the remaining weights are bounded above by the degrees of the syzygies in the resolution.
PB MDPI
SN 2227-7390
YR 2022
FD 2022
LK https://uvadoc.uva.es/handle/10324/61864
UL https://uvadoc.uva.es/handle/10324/61864
LA eng
NO Mathematics, 2022, Vol. 10, Nº. 12, 2079
NO Producción Científica
DS UVaDOC
RD 17-jul-2024