On the number of factorizations of polynomials over finite fields

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:182

Article

Berman, Rachel N.¹  Roth, Ron M.¹ 

[1] Technion, Comp Sci Dept, IL-3200003 Haifa, Israel

关键词: Enumerating divisors of polynomials;    Polynomial factorization;    Polynomials over finite fields;   

DOI  :  10.1016/j.jcta.2021.105462

来源: Elsevier

【 摘 要 】

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). (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free