Classification of Permutation Polynomials of the Form <i>x</I><sup>3< of F<sub><i>q</I>2< Where <i>g</I>(<i>x< = <i>x</I><sup>3< + <i>bx</I> Plus <i>c</I> and <i>b</I>, <i>c</I> ∈ F<i><sub>q</Sub><

Abstract

We classify all permutation polynomials of the form x(3) g(x(q-1)) of F-q2 where g(x) = x(3) + bx + c and b, c is an element of F-q*. Moreover we find new examples of permutation polynomials and we correct some contradictory statements in the recent literature. We assume that gcd(3, q -1) = 1 and we use a well known criterion due to Wan and Lidl, Park and Lee, Akbary and Wang, Wang, and Zieve.