A Recursive Construction of Permutation Polynomials over $\mathbb{F}_{q^2}$ with Odd Characteristic from Rédei Functions

Shihui Fu; Xiutao Feng; Dongdai Lin; Qiang Wang

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arXiv · 1712.07890

A Recursive Construction of Permutation Polynomials over $\mathbb{F}_{q^2}$ with Odd Characteristic from Rédei Functions

Shihui Fu·Xiutao Feng·Dongdai Lin·Qiang Wang

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Abstract

In this paper, we construct two classes of permutation polynomials over $\mathbb{F}_{q^2}$ with odd characteristic from rational Rédei functions. A complete characterization of their compositional inverses is also given. These permutation polynomials can be generated recursively. As a consequence, we can generate recursively permutation polynomials with arbitrary number of terms. More importantly, the conditions of these polynomials being permutations are very easy to characterize. For wide applications in practice, 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 very large.

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Shihui Fu, Xiutao Feng, Dongdai Lin, Qiang Wang. 2017-12-21. A Recursive Construction of Permutation Polynomials over $\mathbb{F}_{q^2}$ with Odd Characteristic from Rédei Functions. https://arxiv.org/abs/1712.07890

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