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Some classes of permutation polynomials over finite fields with odd characteristic

  • Qian Liu
  • Yujuan Sun
  • WeiGuo Zhang
Original Paper
  • 133 Downloads

Abstract

Permutation polynomials have important applications in cryptography, coding theory, combinatorial designs, and other areas of mathematics and engineering. Finding new classes of permutation polynomials is therefore an interesting subject of study. In this paper, for an integer s satisfying \(s=\frac{q^n-1}{2}+q^r\), we give six classes of permutation polynomials of the form \((ax^{q^m}-bx+\delta )^s+L(x)\) over \(\mathbb {F}_{q^n}\), and for s satisfying \(s(p^m-1)\equiv p^m-1\ (mod\ p^n-1)\) or \(s(p^{{\frac{k}{2}}m}-1)\equiv p^{km}-1 (mod\ p^n-1)\), we propose three classes of permutation polynomials of the form \((aTr_m^n(x)+\delta )^s+L(x)\) over \(\mathbb {F}_{p^n}\), respectively.

Keywords

Finite fields Permutation polynomial Trace functions 

Mathematics Subject Classification

11T06 11T71 05A05 

Notes

Acknowledgements

The authors are grateful to the anonymous reviewers for their careful reading of the original version of this paper, their detailed comments and suggestions, which have much improved the quality of this paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Integrated Services NetworksXidian UniversityXi’anChina
  2. 2.State Key Laboratory of CryptogralogyBeijingChina

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