2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | A.1.1 | ||
| Paper Title | On the number of factorizations of polynomials over finite fields | ||
| Authors | Rachel N Berman, Ron M Roth, Technion, Israel | ||
| Session | A.1: Algebraic Coding Theory I | ||
| Presentation | Lecture | ||
| Track | Algebraic and Combinatorial Coding Theory | ||
| Manuscript | Click here to download the manuscript | ||
| Virtual Presentation | Click here to watch in the Virtual Symposium | ||
| 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 (resp., n). | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
