Next Article in Journal
Nonlinearities in Elliptic Curve Authentication
Previous Article in Journal
Strategic Islands in Economic Games: Isolating Economies From Better Outcomes
Article Menu

Export Article

Open AccessArticle
Entropy 2014, 16(9), 5122-5143; doi:10.3390/e16095122

Entropy of Closure Operators and Network Coding Solvability

School of Engineering and Computing Sciences, Durham University, South Road, DH1 3LE, Durham, UK
Received: 17 June 2014 / Revised: 16 August 2014 / Accepted: 11 September 2014 / Published: 25 September 2014
(This article belongs to the Section Information Theory)
View Full-Text   |   Download PDF [242 KB, uploaded 24 February 2015]   |  

Abstract

The entropy of a closure operator has been recently proposed for the study of network 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 axioms for matroids based on their closure operators. We also determine necessary conditions for a large class of closure operators to be solvable. We then define the Shannon entropy of a closure 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. View Full-Text
Keywords: closure operators; entropy; network coding; information inequalities closure operators; entropy; network coding; information inequalities
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top