Some new results on permutation polynomials over finite fields |
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Authors: | Jingxue Ma Tao Zhang Tao Feng Gennian Ge |
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Institution: | 1.School of Mathematical Sciences,Zhejiang University,Hangzhou,China;2.School of Mathematical Sciences,Capital Normal University,Beijing,China;3.Beijing Center for Mathematics and Information Interdisciplinary Sciences,Beijing,China |
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Abstract: | Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, four classes of monomial complete permutation polynomials and one class of trinomial complete permutation polynomials are presented, one of which confirms a conjecture proposed by Wu et al. (Sci China Math 58:2081–2094, 2015). Furthermore, we give two classes of permutation trinomial, and make some progress on a conjecture about the differential uniformity of power permutation polynomials proposed by Blondeau et al. (Int J Inf Coding Theory 1:149–170, 2010). |
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