A new approach to permutation polynomials over finite fields

作者：Hou Xiang Dong^*

来源：Finite Fields and Their Applications, 2012, 18(3): 492-521.

DOI：10.1016/j.ffa.2011.11.002

• Finite field
• Permutation polynomial
• Reversed Dickson polynomial

Let p be a prime and q = p(kappa). We study the permutation properties of the polynomial g(n,q) is an element of F-p[x] defined by the functional equation E-a is an element of Fq (x + a)(n) = g(n,q)(x(q) - x). The polynomial g(n,q) is a q-ary version of the reversed Dickson polynomial in characteristic 2. We are interested in the parameters (n, e; q) for which g(n,q) is a permutation polynomial (PP) of F-qe. We find several families of such parameters and obtain various necessary conditions on such parameters. Initial results, both theoretical and numerical, indicate that the class g(n,q) contains an abundance of PPs over finite fields, many of which are yet to be explained and understood.

• 出版日期2012-5