Characteristic-Dependent Linear Rank Inequalities With Applications to Network Coding

Two characteristic-dependent linear rank inequalities are given for eight variables. In particular, the first inequality holds for all finite fields whose characteristic is not three and does not in general hold over characteristic three. The second inequality holds for all finite fields whose chara...

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Bibliographic Details
Published inIEEE transactions on information theory Vol. 61; no. 5; pp. 2510 - 2530
Main Authors Dougherty, Randall, Freiling, Eric, Zeger, Kenneth
Format Journal Article
LanguageEnglish
Published New York IEEE 01.05.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
capacity
Coding theory
Cramer-Rao bounds
Electrical engineering
Encoding
Inequality
Network coding
Random variables
Shannon entropy
Upper bound
Variables
vector spaces
Vectors
Shannon entropy
vector spaces
network coding
capacity
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ISSN0018-9448
1557-9654
DOI10.1109/TIT.2015.2403361

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Summary:Two characteristic-dependent linear rank inequalities are given for eight variables. In particular, the first inequality holds for all finite fields whose characteristic is not three and does not in general hold over characteristic three. The second inequality holds for all finite fields whose characteristic is three and does not in general hold over characteristics other than three. Applications of these inequalities to the computation of capacity upper bounds in network coding are demonstrated.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2015.2403361