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arXiv · 1909.12175

Entropic matroids and their representation

Emmanuel Abbe·Sophie Spirkl
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Abstract

This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider $p$-entropic matroids, for which the random variables each have support of cardinality $p$. We draw connections between such entropic matroids and secret-sharing matroids and show that entropic matroids are linear matroids when $p = 2,3$ but not when $p = 9$. Our results leave open the possibility for $p$-entropic matroids to be linear whenever $p$ is prime, with particular cases proved here. Applications of entropic matroids to coding theory and cryptography are also discussed.

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Emmanuel Abbe, Sophie Spirkl. 2019-09-26. Entropic matroids and their representation. https://doi.org/10.3390/e21100948

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