On a conjecture about a class of permutation quadrinomials

09/18/2019

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by   Kangquan Li, et al.

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Very recently, Tu et al. presented a sufficient condition about (a_1,a_2,a_3), see Theorem 1.1, such that f(x) = x^3· 2^m + a_1 x^2^m+1+1+ a_2 x^2^m+2 + a_3 x^3 is a class of permutation polynomials over _2^n with n=2m and m odd. In this present paper, we prove that the sufficient condition is also necessary.