A specific type of permutation and complete permutation polynomials over finite fields

Abstract

In this paper, we study polynomials of the form [Formula: see text], where [Formula: see text] and list all permutation polynomials (PPs) and complete permutation polynomials (CPPs) of this form. This type of polynomials were studied by Bassalygo and Zinoviev for the cases [Formula: see text] and [Formula: see text], Wu, Li, Helleseth and Zhang for the case [Formula: see text], [Formula: see text], Bassalygo and Zinoviev answered the question for the case [Formula: see text], [Formula: see text] and finally by Bartoli et al. for the case [Formula: see text]. Here, we determine all PPs and CPPs for the case [Formula: see text].