On a conjecture about a class of permutation quadrinomials

摘要

Very recently, Tu et al. presented a sufficient condition on (a(1), a(2), a(3)), see Theorem 1.1, such that f(x) = x(3 center dot 2m) + a(1)x(2m+1+1) + a(2)x(2m+2) + a(3)x(3) is a class of permutation polynomials over F-2n with n = 2m and m odd. In this present paper, we prove that the sufficient condition is also necessary. (C) 2020 Elsevier Inc. All rights reserved.