A conjecture on permutation trinomials over finite fields of characteristic two

Nian Li; Qiaoyu Hu

doi:10.3934/amc.2019031

Article Contents

2019, Volume 13, Issue 3: 505-512. Doi: 10.3934/amc.2019031

This issue Previous Article A spectral characterisation of

$ t $

-designs and its applications Next Article Galois extensions, positive involutions and an application to unitary space-time coding

A conjecture on permutation trinomials over finite fields of characteristic two

Nian Li^1,2, and
Qiaoyu Hu^1,

1.
Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China
2.
State Key Laboratory of Cryptology, P.O. Box 5159, Beijing 100878, China

Received: August 2018

Published: August 2019

This work was supported by the National Natural Science Foundation of China (Nos.61702166, 61761166010) and the National Natural Science Foundation of Hubei Province of China (No. 2017CFB143)

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Abstract

In this paper, by analyzing the quadratic factors of an $ 11 $-th degree polynomial over the finite field $ {\mathbb F}_{2^n} $, a conjecture on permutation trinomials over $ {\mathbb F}_{2^n}[x] $ proposed very recently by Deng and Zheng is settled, where $ n = 2m $ and $ m $ is a positive integer with $ \gcd(m,5) = 1 $.

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Mathematics Subject Classification: Primary: 05A05; Secondary: 11T06, 11T55.

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