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Entropy of Closure Operators and Network Coding Solvability

Gadouleau, Maximilien

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The entropy of a closure operator has been recently proposed for the study ofnetwork coding and secret sharing. In this paper, we study closure operators in relation to their entropy. We first introduce four different kinds of rank functions for a given closure operator, which determine bounds on the entropy of that operator. This yields new axiomsfor matroids based on their closure operators. We also determine necessary conditions fora large class of closure operators to be solvable. We then define the Shannon entropy of aclosure operator and use it to prove that the set of closure entropies is dense. Finally, we justify why we focus on the solvability of closure operators only.


Gadouleau, M. (2014). Entropy of Closure Operators and Network Coding Solvability. Entropy, 16(9), 5122-5143.

Journal Article Type Article
Publication Date Sep 25, 2014
Deposit Date Sep 25, 2014
Publicly Available Date Sep 25, 2014
Journal Entropy
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 16
Issue 9
Pages 5122-5143
Keywords Closure operators, Entropy, Network coding, Information inequalities.


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