Common information, matroid representation, and secret sharing for matroid ports
Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have been found, it seems that most of them remain undiscovered. Improved results have been obtained in recent works by using...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 2020 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/355377 |
| Online Access: | https://hdl.handle.net/2117/355377 https://dx.doi.org/10.1007/s10623-020-00811-1 |
| Access Level: | Open access |
| Keyword: | Cryptography Coding theory Matroid representation Secret sharing Information inequalities Common information Linear programming Criptografia Codificació, Teoria de la Classificació AMS::94 Information And Communication, Circuits::94A Communication, information Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
| Summary: | Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have been found, it seems that most of them remain undiscovered. Improved results have been obtained in recent works by using the properties from which they are derived instead of the inequalities themselves. We apply here this strategy to the classification of matroids according to their representations and to the search for bounds on secret sharing for matroid ports. |
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