Classification of some quadrinomials over finite fields of odd characteristic |
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Institution: | 1. Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey;2. Department of Mathematics, At?l?m University, Ankara, Turkey;1. School of Mathematics, Shandong University, Jinan, 250100, China;2. Hubei Key Laboratory of Applied Mathematics, School of Cyber Science and Technology, Hubei University, Wuhan, 430062, China;3. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China;1. Department of Mathematics and Computer Science, Santa Clara University, 500 El Camino Real, 95053, USA;2. Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada;1. Dipartimento di Matematica, Università degli studi di Trento, Italy;2. College of Science, National University of Defense Technology, Changsha, 410073, China;1. School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, China;2. School of Mathematics and Information, China West Normal University, Nanchong, Sichuan, 637002, China;3. Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China;4. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;5. School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang, 310018, China |
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Abstract: | In this paper, we completely determine all necessary and sufficient conditions such that the polynomial , where , is a permutation quadrinomial of over any finite field of odd characteristic. This quadrinomial has been studied first in 25] by Tu, Zeng and Helleseth, later in 24] Tu, Liu and Zeng revisited these quadrinomials and they proposed a more comprehensive characterization of the coefficients that results with new permutation quadrinomials, where and finally, in 16], Li, Qu, Li and Chen proved that the sufficient condition given in 24] is also necessary and thus completed the solution in even characteristic case. In 6] Gupta studied the permutation properties of the polynomial , where and and proposed some new classes of permutation quadrinomials of .In particular, in this paper we classify all permutation polynomials of of the form , where , over all finite fields of odd characteristic and obtain several new classes of such permutation quadrinomials. |
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Keywords: | Permutation polynomials Finite fields Absolutely irreducible |
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