Abstract

PENA-MACIAS, Victor  and  SARRIA-ZAPATA, Humberto. Characteristic-Dependent Linear Rank Inequalities in 21 Variables. Rev. acad. colomb. cienc. exact. fis. nat. [online]. 2019, vol.43, n.169, pp.764-770. ISSN 0370-3908.  https://doi.org/10.18257/raccefyn.928.

In Linear Algebra over finite fields, a characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of spans of vector subspaces of a finite dimensional vector space over a finite field of determined characteristic, and does not in general hold over fields with other characteristic. This paper shows a preliminary result in the production of these inequalities. We produce three new inequalities in 21 variables using as guide a particular binary matrix, with entries in a finite field, whose rank is 8, with characteristic 2; 9 with characteristic 3; or 10 with characteristic neither 2 nor 3. The first inequality is true over fields whose characteristic is 2; the second inequality is true over fields whose characteristic is 2 or 3; the third inequality is true over fields whose characteristic is neither 2 nor 3.

Keywords : Entropy; Linear rank inequality; Binary matrix; Direct sum in vector spaces.

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