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The sum of modules of Walsh coefficients of Boolean functions

  • Reynier A. de la Cruz Jimenez and Oleg V. Kamlovskiy EMAIL logo
Published/Copyright: November 8, 2016
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Discrete Mathematics and Applications
From the journal Discrete Mathematics and Applications Volume 26 Issue 5

Abstract

We obtain achievable lower and upper bounds for the sums of modules of Walsh coefficients of Boolean functions of nvariables. An average value of such sums in the class of all Boolean functions of n variables and in its subclass consisting of all balanced functions is evaluated. We present some classes of nonlinear balanced functions whose sums of modules of Walsh coefficients are close to the obtained lower and upper bounds

keywords: Boolean functions; Walsh coefficients; filtering generators

Originally published in Diskretnaya Matematika (2015) 27, №4, 49–66 (in Russian).

References

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Received: 2015-8-7
Published Online: 2016-11-8
Published in Print: 2016-10-1

© 2016 Walter de Gruyter GmbH, Berlin/Boston

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  2. Research Article
  3. A generalization of Ore’s theorem on polynomials
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  5. The sum of modules of Walsh coefficients of Boolean functions
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https://doi.org/10.1515/dma-2016-0023
Keywords for this article
Boolean functions; Walsh coefficients; filtering generators

Articles in the same Issue

  1. Frontmatter
  2. Research Article
  3. A generalization of Ore’s theorem on polynomials
  4. Research Article
  5. The sum of modules of Walsh coefficients of Boolean functions
  6. Research Article
  7. The algorithm for identical object searching with bounded worst-case complexity and linear memory
  8. Research Article
  9. Tests of contact closure for contact circuits
  10. Research Article
  11. Orbital derivatives over subgroups and their combinatorial and group-theoretic properties
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