A Note on a Class of Quadratic Permutations over F2n

Finding new classes of permutation polynomials is a challenging problem. Blockhuis at al. investigated the permutation behavior of polynomials of the form Σi=0 n-1 aiX2i+1 over F2n. In this paper, we extend their results and propose as a new conjecture that if n= 2e then X2 is the only unitary permutation polynomial of this type.