# How to Find New Characteristic-Dependent Linear Rank Inequalities using Binary Matrices as a Guide

@article{Pea2019HowTF, title={How to Find New Characteristic-Dependent Linear Rank Inequalities using Binary Matrices as a Guide}, author={Victor Pe{\~n}a and Humberto Sarria}, journal={ArXiv}, year={2019}, volume={abs/1905.00003} }

In Linear Algebra over finite fields, a characteristic-dependent 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{n-1}{2}\right\rfloor -4…

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Common information, matroid representation, and secret sharing for matroid ports

- Computer Science, MathematicsDes. Codes Cryptogr.
- 2021

Improved results have been obtained in recent works by using the properties from which they are derived instead of the inequalities themselves to the classification of matroids according to their representations and the search for bounds on secret sharing for matroid ports.

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