A Class of Permutation Binomials over Finite Fields

2012/10/02 by Xiang‐dong Hou, Hou, Xiang-dong
Computer Science · Mathematics · #11T06 #11T55 #33C05 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1210.0881

openalex publication_date 2012/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let q>2 be a prime power and f=\tt x^q-2+t\tt x^q2-q-1, where t∈\Bbb F_q^*. It was recently conjectured that f is a permutation polynomial of \Bbb F_q² if and only if one of the following holds: (i) t=1, q≡ 1\pmod 4; (ii) t=-3, q≡ ±1\pmod12; (iii) t=3, q≡ -1\pmod 6. We confirm this conjecture in the present paper.

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