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A Complete Characterization of Plateaued Boolean Functions in Terms of Their Cayley Graphs

  • Constanza Riera
  • Patrick Solé
  • Pantelimon Stănică
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10831)

Abstract

In this paper we find a complete characterization of plateaued Boolean functions in terms of the associated Cayley graphs. Precisely, we show that a Boolean function f is s-plateaued (of weight \(=2^{(n+s-2)/2}\)) if and only if the associated Cayley graph is a complete bipartite graph between the support of f and its complement (hence the graph is strongly regular of parameters \(e=0,d=2^{(n+s-2)/2}\)). Moreover, a Boolean function f is s-plateaued (of weight \(\ne 2^{(n+s-2)/2}\)) if and only if the associated Cayley graph is strongly 3-walk-regular (and also strongly \(\ell \)-walk-regular, for all odd \(\ell \ge 3\)) with some explicitly given parameters.

Keywords

Plateaued Boolean functions Cayley graphs Strongly regular Walk regular 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computing, Mathematics, and PhysicsWestern Norway University of Applied SciencesBergenNorway
  2. 2.CNRS/LAGA, University of Paris 8Saint-DenisFrance
  3. 3.Department of Applied MathematicsNaval Postgraduate SchoolMontereyUSA

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