On the Number of Factorizations of Polynomials over Finite Fields
| Autor: | Rachel N. Berman, Ron M. Roth |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Discrete mathematics
FOS: Computer and information sciences Polynomial Discrete Mathematics (cs.DM) Computer Science - Information Theory Information Theory (cs.IT) 020206 networking & telecommunications 02 engineering and technology Theoretical Computer Science Combinatorics Finite field Computational Theory and Mathematics FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Enumeration Discrete Mathematics and Combinatorics Mathematics - Combinatorics Combinatorics (math.CO) Computer Science - Discrete Mathematics Mathematics |
| Zdroj: | ISIT |
| DOI: | 10.1109/isit44484.2020.9174405 |
| Popis: | 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). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|