How to Find New CharacteristicDependent Linear Rank Inequalities using Binary Matrices as a Guide
Abstract
In Linear Algebra over finite fields, a characteristicdependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold over other characteristics. In this paper, we show a method to produce these inequalities using binary matrices with suitable ranks over different fields. In particular, for each $n\geq7$, we produce $2\left\lfloor \frac{n1}{2}\right\rfloor 4$ characteristicdependent linear rank inequalities over $n$ variables. Many of the inequalities obtained are new but some of them imply the inequalities presented in [1,9].
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1905.00003
 Bibcode:
 2019arXiv190500003P
 Keywords:

 Computer Science  Information Theory;
 68P30
 EPrint:
 arXiv admin note: text overlap with arXiv:1903.11587