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A class of permutation trinomials over finite fields

Volume 162 / 2014

Xiang-dong Hou Acta Arithmetica 162 (2014), 51-64 MSC: Primary 11T06; Secondary 11T55. DOI: 10.4064/aa162-1-3


Let $q>2$ be a prime power and $f=-{\tt x}+t{\tt x}^q+{\tt x}^{2q-1}$, where $t\in \mathbb F_q^*$. We prove that $f$ is a permutation polynomial of $\mathbb F_{q^2}$ if and only if one of the following occurs: (i) $q$ is even and $\text {Tr}_{q/2}({{1}/t})=0$; (ii) $q\equiv 1\ ({\rm mod} 8)$ and $t^2=-2$.


  • Xiang-dong HouDepartment of Mathematics and Statistics
    University of South Florida
    Tampa, FL 33620, U.S.A.

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