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arXiv · 2203.17194

Free Resolutions and Generalized Hamming Weights of binary linear codes

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

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.

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Ignacio García-Marco, Irene Márquez-Corbella, Edgar Martínez-Moro, Yuriko Pitones. 2022-03-31. Free Resolutions and Generalized Hamming Weights of binary linear codes. https://arxiv.org/abs/2203.17194

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