New results on permutation polynomials over finite fields

作者：Qin, Xiaoer; Qian, Guoyou; Hong, Shaofang^*

来源：International Journal of Number Theory, 2015, 11(2): 437-449.

DOI：10.1142/S1793042115500220

• Permutation polynomial
• linearized polynomial
• linear translator
• matrix

In this paper, we get several new results on permutation polynomials over finite fields. First, by using the linear translator, we construct permutation polynomials of the forms L(x) + Sigma(k)(j)(= 1) gamma(j)h(j)(f(j) (x)) and x + Sigma(k)(j)(= 1) gamma(j)f(j) (x). These forms generalize the results obtained by Kyureghyan in 2011. Consequently, we characterize permutation polynomials of the form L(x) + Sigma(l)(i)(= 1) gamma iTrFqm/F-q (h(i)(x)), which extends a theorem of Charpin and Kyureghyan obtained in 2009.

• 出版日期2015-3
• 单位四川大学; 长江师范学院