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On Plateaued Functions, Linear Structures and Permutation Polynomials

  • Sihem Mesnager
  • Kübra Kaytancı
  • Ferruh ÖzbudakEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11445)

Abstract

We obtain concrete upper bounds on the algebraic immunity of a class of highly nonlinear plateaued functions without linear structures than the one was given recently in 2017, Cusick. Moreover, we extend Cusick’s class to a much bigger explicit class and we show that our class has better algebraic immunity by an explicit example. We also give a new notion of linear translator, which includes the Frobenius linear translator given in 2018, Cepak, Pasalic and Muratović-Ribić as a special case. We find some applications of our new notion of linear translator to the construction of permutation polynomials. Furthermore, we give explicit classes of permutation polynomials over \(\mathbb {F}_{q^n}\) using some properties of \(\mathbb {F}_q\) and some conditions of 2011, Akbary, Ghioca and Wang.

Keywords

Plateaued functions Linear structure Permutation polynomials 

Notes

Acknowledgments

We thank the reviewers for their insightful and fruitful remarks which greatly improved the presentation of the paper.

The research of the second and third authors has been funded by METU Coordinatorship of Scientific Research Projects via grant for projects GAP-101-2018-2782.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.LAGA, UMR 7539, CNRS, University Paris XIII - Sorbonne Paris Cité, University Paris VIII (Department of Mathematics) and Telecom ParisTechParisFrance
  2. 2.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey
  3. 3.Department of Mathematics and Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey

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