A Class of Permutation Trinomials over Finite Fields

2013/03/03 by Hou, Xiang-dong
#11T06 #11T55 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1303.0568

Abstract

Let q>2 be a prime power and f=-\tt x+t\tt x^q+\tt x^2q-1, where t∈\Bbb F_q^*. We prove that f is a permutation polynomial of \Bbb F_q² if and only if one of the following occurs: (i) q is even and Tr_q/2(\frac 1t)=0; (ii) q≡ 1\pmod 8 and t²=-2.

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