General constructions of permutation polynomials of the form (x2m x + δ)i(2m-1)+1 + x over F22m

Recently, there has been a lot of work on constructions of permutation polynomials of the form (x(2m) + x + delta)(s) + x over the finite field F(2)2m, especially in the case when s is of the form s = i(2(m) - 1) + 1 (Niho exponent). In this paper, we further investigate permutation polynomials with this form. Instead of seeking for sporadic construction of the parameter i, we give two general sufficient conditions on i such that (x(2m) + x + delta(2(m) - 1)+1 + x permutes F(2)2m: (i) (2(k) + 1)(i) equivalent to 1 or 2(k) (mod 2(m) + 1); (ii) (2(k) - 1)(i) equivalent to 1 or 2(k) (mod 2(m) + 1), where 1 <= k <= m - 1 is any integer. It turns out that most of previous constructions of the parameter i are covered by our results, and they yield many new classes of permutation polynomials as well. (C) 2018 Elsevier Inc. All rights reserved.