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Some new results on permutation polynomials over finite fields (1506.05525v3)
Published 18 Jun 2015 in cs.IT, math.IT, and math.NT
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., to appear. Doi: 10.1007/s11425-014-4964-2). Furthermore, we give two classes of trinomial permutation polynomials, 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, 2010, 1, pp. 149-170).