On the Number of Factorizations of Polynomials over Finite Fields
Discrete Mathematics
2021-04-10 v2 Information Theory
Combinatorics
math.IT
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).
Cite
@article{arxiv.2004.03058,
title = {On the Number of Factorizations of Polynomials over Finite Fields},
author = {Rachel N. Berman and Ron M. Roth},
journal= {arXiv preprint arXiv:2004.03058},
year = {2021}
}