Unimodular Polynomial Matrices over Finite Fields

2019/07/10 by Arora, Akansha, Ram, Samrith, Venkateswarlu, Ayineedi
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.04642

Abstract

We consider some combinatorial problems on matrix polynomials over finite fields. Using results from control theory we give a proof of a result of Helmke, Jordan and Lieb on the number of linear unimodular matrix polynomials over a finite field. As an application of our results we give a new proof of a theorem of Chen and Tseng which answers a question of Niederreiter on splitting subspaces. We use our results to affirmatively resolve a conjecture on the probability that a matrix polynomial is unimodular.

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