Permutation Polynomials with Carlitz Rank 2

Abstract

Let ${\mathbb{F}}_q$ denote the finite field with $q$ elements. The Carlitz rank of a permutation polynomial is a important measure of complexity of the polynomial. In this paper we find the sharp lower bound for the weight of any permutation polynomial with Carlitz rank $2$, improving the bound found by Gómez-Pérez, Ostafe and Topuzoğlu in that case.

10 pages, comments are welcome