Session S26 - Finite fields and applications

Tuesday, July 20, 19:00 ~ 19:50 UTC-3

Open Problems for Polynomials over Finite Fields

Daniel Panario

Carleton University, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We focus only on univariate polynomials over a finite field. We first comment on the existence and number of several classes of polynomials. Open problems are theoretical.

Then, we center in low-weight (irreducible) polynomials. The conjectures here are practically oriented.

Next, we focus on the dynamics of iterating functions over finite fields and their periodicity and permutational implications.

Finally, time allowing, we give brief descriptions of a selection of open problems from several classical areas of research including factorization of polynomials, special polynomials (permutations, PN/APN functions), and relations between integer numbers and polynomials.

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