How to Find New Characteristic-Dependent Linear Rank Inequalities using Binary Matrices as a Guide
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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≥7, we produce 2n-1/2 -4 characteristic-dependent linear rank inequalities over n variables. Many of the inequalities obtained are new but some of them imply the inequalities presented in [1,9].
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