[IEEE Trans. on Information Theory, May 2015, pp. 2510-2530 ]
Characteristic-Dependent Linear Rank Inequalities with Applications to Network Coding
Randall Dougherty, Eric Freiling, and Kenneth Zeger
Abstract
Two characteristic-dependent linear rank inequalities are given for eight variables.
Specifically, 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.