Unimodular polynomial matrices over finite fields

Article Type

Research Article

Publication Title

Journal of Algebraic Combinatorics

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 Lieb, Jordan and Helmke 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.

First Page

1299

Last Page

1312

DOI

10.1007/s10801-020-00963-2

Publication Date

6-1-2021

Comments

Open Access, Green

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