Several classes of complete permutation polynomials with Niho exponents

Abstract In this paper, eight classes of complete permutation polynomials with Niho exponents are proposed. Based on certain polynomials over F q 2 whose ( q − 1 ) -th powers are 1 or monomials on the unit circle, three classes of complete permutation polynomials are obtained. In addition, we completely characterize the complete permutation properties of five classes of known permutation trinomials.