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Paper IDA.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).

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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