On permutation polynomials over finite fields of characteristic 2

Let 𝔽2t denotes the finite field of order 2t where t > 1. A permutation polynomial f(x) over 𝔽2t with f(0) = 0 and f(1) = 1 such that for each v ∈ 𝔽2t,fv(x) = f(x+v)+f(v) x is a permutation polynomial satisfying fv(0) = 0 is called a o-polynomial. In this paper, we determine all o-polynomials up to degree 8.