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Determination of a type of permutation binomials and trinomials

  • R. K. SharmaEmail author
  • Rohit Gupta
Original Paper

Abstract

Let \({\mathbb {F}}_q\) denote the finite field of order q. In this paper, we determine certain permutation binomials and permutation trinomials of the form \(x^{r}h(x^{q+1})\) over \(\mathbb {F}_{q^2}\). Some of them are generalizations of known ones.

Keywords

Finite field Permutation polynomial Permutation binomial Permutation trinomial 

Mathematics Subject Classification

11T06 11T55 

Notes

Acknowledgements

The authors gratefully acknowledge the valuable suggestions from the anonymous referees which improved the quality and presentation of the paper. The first author is ConsenSys Block Chain Chair Professor. He wants to thank the CosenSys AG for the same. The second author wants to thank for its support, CSIR, New Delhi, Govt. of India, Grant No. F.No. 09/086(1135)/2012-EMR-I.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology, DelhiNew DelhiIndia

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