On permutation quadrinomials from Niho exponents in characteristic two

Recently Zheng et al. [18] characterized the coefficients of f(x)=x+a1xs1(2m−1)+1+a2xs2(2m−1)+1+a3xs3(2m−1)+1 over F22m that lead f(x) to be a permutation of F22m for (s1,s2,s3)=(14,1,34). They left open the question whether those conditions were also necessary. In this paper, we give a positive answer to that question, solving their conjecture.