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arXiv · 2004.03058

On the Number of Factorizations of Polynomials over Finite Fields

Rachel N. Berman·Ron M. Roth
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Abstract

Motivated by coding applications,two enumeration problems are considered: the number of distinct divisors of a degree-m polynomial over F = GF(q), and the number of ways a polynomial can be written as a product of two polynomials of degree at most n over F. For the two problems, bounds are obtained on the maximum number of factorizations, and a characterization is presented for polynomials attaining that maximum. Finally, expressions are presented for the average and the variance of the number of factorizations, for any given m (respectively, n).

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BibTeXRIS

Rachel N. Berman, Ron M. Roth. 2020-04-07. On the Number of Factorizations of Polynomials over Finite Fields. https://doi.org/10.1016/j.jcta.2021.105462

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