2026-05-15T05:41:07Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/618642025-02-21T10:44:53Zcom_10324_1145com_10324_931com_10324_894col_10324_1254
García Marco, Ignacio
Marquez Corbella, Irene
Martínez Moro, Edgar
Pitones, Yuriko
2023-10-02T12:39:11Z
2023-10-02T12:39:11Z
2022
Mathematics, 2022, Vol. 10, Nº. 12, 2079
2227-7390
https://uvadoc.uva.es/handle/10324/61864
10.3390/math10122079
2079
12
Mathematics
10
2227-7390
Producción Científica
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.
Ministerio de Ciencia e Innovación/Agencia Estatal de Investigación (AEI)/10.13039/501100011033 and ULL Research Projects - (grant PID2019- 105896GB-I00)
Ministerio de Ciencia e Innovación/Agencia Estatal de Investigación (AEI)/10.13039/501100011033 y Fondo Europeo de Desarrollo Regional (FEDER) - (Grant PGC2018-096446-B-C21)
application/pdf
eng
MDPI
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
© 2022 The Authors
Atribución 4.0 Internacional
Algebraic geometry
Free resolution
Computer science
Mathematics
Códificación (Informática)
Computer systems
Generalized Hamming weight
Pesos Hamming generalizados
1201.01 Geometría Algebraica
1203.17 Informática
12 Matemáticas
Free resolutions and generalized Hamming weights of binary linear codes
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
https://www.mdpi.com/2227-7390/10/12/2079
SI