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Mathematics in Computer Science

, Volume 12, Issue 3, pp 349–369 | Cite as

Boolean Functions: Degree and Support

  • Joan-Josep ClimentEmail author
  • Francisco J. García
  • Verónica Requena
Article
  • 66 Downloads

Abstract

In this paper we establish some properties about Boolean functions that allow us to relate their degree and their support. These properties allow us to compute the degree of a Boolean function without having to calculate its algebraic normal form. Furthermore, we introduce some linear algebra properties that allow us to obtain the degree of a Boolean function from the dimension of a linear or affine subspace. Finally we derive some algorithms and compute the average time to obtain the degree of some Boolean functions from its support.

Keywords

Boolean function Support Weight Algebraic normal form Degree Linear space 

Mathematics Subject Classification

06E30 94A60 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Joan-Josep Climent
    • 1
    Email author
  • Francisco J. García
    • 2
  • Verónica Requena
    • 1
  1. 1.Departament de MatemàtiquesUniversitat d’AlacantSant Vicent del RaspeigSpain
  2. 2.Departament de Fonaments de l’Anàlisi EconòmicaUniversitat d’AlacantSant Vicent del RaspeigSpain

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