In this paper, we construct two classes of permutation polynomials over Fq2 with odd characteristic closely related to rational Rédei functions. Two distinct characterizations of their compositional inverses are also obtained. These permutation polynomials can be generated recursively. As a consequence, we can generate permutation polynomials with an arbitrary number of terms in a very simple way. Moreover, several classes of permutation binomials and trinomials are given. With the help of a computer, we find that the number of permutation polynomials of these types is quite big.

Compositional inverse, Dickson polynomials, Finite fields, Permutation polynomials, Rédei functions
dx.doi.org/10.1007/s10623-018-0548-4
Designs, Codes and Cryptography
School of Mathematics and Statistics

Fu, S. (Shihui), Feng, X. (Xiutao), Lin, D. (Dongdai), & Wang, Q. (2018). A recursive construction of permutation polynomials over Fq2 with odd characteristic related to Rédei functions. Designs, Codes and Cryptography. doi:10.1007/s10623-018-0548-4