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Designs, Codes and Cryptography

, Volume 87, Issue 7, pp 1481–1498 | Cite as

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

  • Shihui Fu
  • Xiutao Feng
  • Dongdai Lin
  • Qiang WangEmail author
Article

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.

Keywords

Finite fields Permutation polynomials Compositional inverse Rédei functions Dickson polynomials 

Mathematics Subject Classification

11T06 11T55 05A05 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Shihui Fu
    • 1
  • Xiutao Feng
    • 1
    • 2
  • Dongdai Lin
    • 3
  • Qiang Wang
    • 4
    Email author
  1. 1.Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.Science and Technology on Communication Security LaboratoryChengduChina
  3. 3.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  4. 4.School of Mathematics and StatisticsCarleton UniversityOttawaCanada

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