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 (x2m+x+δ)s+x over the finite field F22m, especially in the case when s is of the form s=i(2m−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 (x2m+x+δ)i(2m−1)+1+x permutes F22m: (i) (2k+1)i≡1or2k(mod2m+1); (ii) (2k−1)i≡−1or2k(mod2m+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.