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09/18/2023
On the Minimum Distance, Minimum Weight Codewords, and the Dimension of Projective Reed-Muller Codes
We give an alternative proof of the formula for the minimum distance of ...
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01/30/2021
On the Purity of Resolutions of Stanley-Reisner Rings Associated to Reed-Muller Codes
Following Johnsen and Verdure (2013), we can associate to any linear cod...
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04/07/2020
Arithmetic, Geometry, and Coding Theory: Homage to Gilles Lachaud
We give an overview of several of the mathematical works of Gilles Lacha...
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02/05/2020
Pure Resolutions, Linear Codes, and Betti Numbers
We consider the minimal free resolution of Stanley-Reisner rings associa...
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04/03/2019
A Polymatroid Approach to Generalized Weights of Rank Metric Codes
We consider the notion of a (q,m)-polymatroid, due to Shiromoto, and the...
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09/12/2018