Several classes of permutation trinomials over \(\mathbb {F}_{5^{n}}\) from Niho exponents

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Abstract

The construction of permutation trinomials over finite fields attracts people’s interest recently due to their simple form and some additional properties. Motivated by some results on the construction of permutation trinomials with Niho exponents, in this paper, by constructing some new fractional polynomials that permute the set of the (q + 1)-th roots of unity in \(\mathbb {F}_{q^{2}}\), we present several classes of permutation trinomials with Niho exponents over \(\mathbb {F}_{q^{2}}\), where q = 5 k .

Keywords

Finite fields Permutation polynomials Trinomials Niho exponents 

Mathematics Subject Classification (2010)

05A05 11T06 

Notes

Acknowledgements

The authors would like to thank the referees for their comments that improved the presentation and quality of this paper. This work of G. Wu was supported by the Fundamental Research Funds for the Central Universities (No. JB161504) and the National Natural Science Foundation of China (Grants Nos. 61602361, 61671013). This work of N. Li was supported in part by the National Natural Science Foundation of China under Grant 61702166 and the Natural Science Foundation of Hubei Province of China under Grant 2017CFB143.

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Authors and Affiliations

  1. 1.State Key Laboratory of Integrated Service Networks, School of Cyber EngineeringXidian UniversityXi’anChina
  2. 2.Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and StatisticsHubei UniversityWuhanChina
  3. 3.Department of InformaticsUniversity of BergenBergenNorway

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