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A recursive construction of permutation polynomials over \({\mathbb {F}}_{q^2}\) with odd characteristic related to Rédei functions

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Abstract

In this paper, we construct two classes of permutation polynomials over \({\mathbb {F}}_{q^2}\) 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.

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Acknowledgements

We thank the anonymous referees for their helpful suggestions. This work was supported by the National Key Research and Development Program of China (No. 2016YFB0800401), Hubei Provincial Natural Science Foundation of China (2016CFB454), Science and Technology on Communication Security Laboratory (No. 6142103010701), the National Natural Science Foundation of China (Nos. 61572491 and 11688101) and NSERC of Canada.

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Authors and Affiliations

  1. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Shihui Fu & Xiutao Feng

  2. Science and Technology on Communication Security Laboratory, Chengdu, 610041, China

    Xiutao Feng

  3. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Dongdai Lin

  4. School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6, Canada

    Qiang Wang

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  1. Shihui Fu
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  2. Xiutao Feng
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  4. Qiang Wang
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Correspondence to Qiang Wang.

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Communicated by C. Carlet.

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Fu, S., Feng, X., Lin, D. et al. A recursive construction of permutation polynomials over \({\mathbb {F}}_{q^2}\) with odd characteristic related to Rédei functions. Des. Codes Cryptogr. 87, 1481–1498 (2019). https://doi.org/10.1007/s10623-018-0548-4

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