Gadouleau, Maximilien (2014) 'Entropy of closure operators and network coding solvability.', Entropy., 16 (9). pp. 5122-5143.
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.
|Keywords:||Closure operators, Entropy, Network coding, Information inequalities.|
|Full text:||(VoR) Version of Record|
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|Publisher Web site:||http://dx.doi.org/10.3390/e16095122|
|Publisher statement:||© 2014 by the author; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).|
|Date accepted:||No date available|
|Date deposited:||25 September 2014|
|Date of first online publication:||September 2014|
|Date first made open access:||No date available|
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