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On a class of permutation trinomials in characteristic 2

  • Xiang-dong Hou
Article
  • 7 Downloads
Part of the following topical collections:
  1. Special Issue on Boolean Functions and Their Applications

Abstract

Recently, Tu, Zeng, Li, and Helleseth considered trinomials of the form \(f(X)=X+aX^{q(q-1)+ 1}+bX^{2(q-1)+ 1}\in \mathbb {F}_{q^{2}}[X]\), where q is even and \(a,b\in \mathbb {F}_{q^{2}}^{*}\). They found sufficient conditions on a, b for f to be a permutation polynomial (PP) of \(\mathbb {F}_{q^{2}}\) and they conjectured that the sufficient conditions are also necessary. The conjecture has been confirmed by Bartoli using the Hasse-Weil bound. In this paper, we give an alternative solution to the question. We also use the Hasse-Weil bound, but in a different way. Moreover, the necessity and sufficiency of the conditions are proved by the same approach.

Keywords

Finite field Hasse-Weil bound Permutation polynomial 

Mathematics Subject Classification (2010)

11T06 11T55 14H05 

Notes

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Copyright information

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

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA

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