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ACM Communications in Computer Algebra

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Disponibilidad
Institución detectada Período Navegá Descargá Solicitá
No detectada desde ene. 1967 / hasta dic. 2023 ACM Digital Library

Información

Tipo de recurso:

revistas

ISSN electrónico

1932-2240

Editor responsable

Association for Computing Machinery (ACM)

País de edición

Estados Unidos

Tabla de contenidos

Computing generalized hamming weights of binary linear codes via free resolutions

Ignacio García-Marco; Irene Márquez-Corbella; Edgar Martínez-Moro; Yuriko Pitones

<jats:p>In this work, we explore the relationship between free resolution of some monomial ideals and Generalized Hamming Weights (GHWs) of binary codes. More precisely, we look for a structure smaller than the set of codewords of minimal support that provides us some information about the GHWs. We prove that the first and second generalized Hamming weight of a binary linear code can be computed (by means of a graded free resolution) from a set of monomials associated to a binomial ideal related with the code. Moreover, the remaining weights are bounded by the Betti numbers for that set.</jats:p>

Palabras clave: General Medicine.

Pp. 19-24