Publication

Entropic Matroids and Their Representation

Emmanuel Abbé
2019
Article
Résumé

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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