Some results about permutation properties of a kind of binomials over finite fields

06/21/2019

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by   Xiaogang Liu, et al.

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Permutation polynomials have many applications in finite fields theory, coding theory, cryptography, combinatorial design, communication theory, and so on. Permutation binomials of the form x^r(x^q-1+a) over F_q^2 have been studied before, K. Li, L. Qu and X. Chen proved that they are permutation polynomials if and only if r=1 and a^q+1=1. In this paper, we consider the same binomial, but over finite fields F_q^3 and F_q^e. Two different kinds of methods are employed, and some partial results are obtained for them.