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International Workshop on the Arithmetic of Finite Fields

WAIFI 2010: Arithmetic of Finite Fields pp 135–150Cite as

Switching Construction of Planar Functions on Finite Fields

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6087))

Abstract

A function \(f: \mathbb{F}_{p^n}\rightarrow\mathbb{F}_{p^n}\) is planar, if f(x + a) − f(x) = b has precisely one solution for all \(a,b\in\mathbb{F}_{p^n}\), 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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Otto-von-Guericke-University Magdeburg, 39106, Magdeburg, Germany

    Alexander Pott & Yue Zhou

Authors
  1. Alexander Pott
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  2. Yue Zhou
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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    M. Anwar Hasan

  2. Department of Informatics, HIB, University of Bergen, PB 7803, 5020, Bergen, Norway

    Tor Helleseth

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Pott, A., Zhou, Y. (2010). Switching Construction of Planar Functions on Finite Fields. In: Hasan, M.A., Helleseth, T. (eds) Arithmetic of Finite Fields. WAIFI 2010. Lecture Notes in Computer Science, vol 6087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13797-6_10

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  • DOI: https://doi.org/10.1007/978-3-642-13797-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13796-9

  • Online ISBN: 978-3-642-13797-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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