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- W4310431574 abstract "Following Johnsen and Verdure (2013), we can associate to any linear code $C$ an abstract simplicial complex and in turn, a Stanley-Reisner ring $R_C$. The ring $R_C$ is a standard graded algebra over a field and its projective dimension is precisely the dimension of $C$. Thus $R_C$ admits a graded minimal free resolution and the resulting graded Betti numbers are known to determine the generalized Hamming weights of $C$. The question of purity of the minimal free resolution of $R_C$ was considered by Ghorpade and Singh (2020) when $C$ is the generalized Reed-Muller code. They showed that the resolution is pure in some cases and it is not pure in many other cases. Here we give a complete characterization of the purity of graded minimal free resolutions of Stanley-Reisner rings associated to generalized Reed-Muller codes of an arbitrary order." @default.
- W4310431574 created "2022-12-10" @default.
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- W4310431574 date "2021-01-30" @default.
- W4310431574 modified "2023-09-27" @default.
- W4310431574 title "On the Purity of Resolutions of Stanley-Reisner Rings Associated to Reed-Muller Codes" @default.
- W4310431574 doi "https://doi.org/10.48550/arxiv.2102.00308" @default.
- W4310431574 hasPublicationYear "2021" @default.
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