Unimodular polynomial matrices over finite fields
Journal of Algebraic Combinatorics
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.
Arora, Akansha; Ram, Samrith; and Venkateswarlu, Ayineedi, "Unimodular polynomial matrices over finite fields" (2021). Journal Articles. 1958.
Open Access, Green