On a conjecture about a class of permutation quadrinomials期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On a conjecture about a class of permutation quadrinomials

Institution:	1. College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, 410073, China;2. State Key Laboratory of Cryptology, Beijing, 100878, China;3. College of Information Science and Technology, College of Cyber Security, Jinan University, Guangzhou, Guangdong, 510632, China;1. School of Mathematics, Hefei University of Technology, Hefei, 230601, Anhui, People''s Republic of China;2. Intelligent Interconnected systems Laboratory of Anhui province, Hefei, 230009, Anhui, People''s Republic of China;1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China;3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, United States;4. Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, China

Abstract:	Very recently, Tu et al. presented a sufficient condition on $(a_{1}, a_{2}, a_{3})$ , see Theorem 1.1, such that $f (x) = x^{3 ? 2^{m}} + a_{1} x^{2^{m + 1} + 1} + a_{2} x^{2^{m} + 2} + a_{3} x^{3}$ is a class of permutation polynomials over $F_{2^{n}}$ with $n = 2 m$ and m odd. In this present paper, we prove that the sufficient condition is also necessary.

Keywords:	Permutation polynomials Permutation quadrinomials Finite fields Hasse-Weil bounds
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