A Note on a Class of Quadratic Permutations over ${\mathbb F}_{{2^n}}$

Abstract

Finding new classes of permutation polynomials is a challenging problem. Blockhuis at al. investigated the permutation behavior of polynomials of the form \(\sum_{i=0}^{n-1}a_iX^{2^i+1}\) over \({\mathbb F}_{{2^n}}\). In this paper, we extend their results and propose as a new conjecture that if n = 2e then X 2 is the only unitary permutation polynomial of this type.