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.

Additional Metadata
Keywords Compositional inverse, Dickson polynomials, Finite fields, Permutation polynomials, Rédei functions
Persistent URL dx.doi.org/10.1007/s10623-018-0548-4
Journal Designs, Codes and Cryptography
Citation
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