Switching construction of planar functions on finite fields

  • Authors:
  • Alexander Pott;Yue Zhou

  • Affiliations:
  • Department of Mathematics, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany;Department of Mathematics, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany

  • Venue:
  • WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
  • Year:
  • 2010

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Abstract

A function f : Fpn → Fpn is planar, if f(x+a)-f(x) = b has precisely one solution for all a, b ε Fpn, a ≠ 0. In this paper, we discuss possible extensions of the switching idea developed in [1] to the case of planar functions. We show that some of the known planar functions can be constructed from each other by switching.