Startseite The sum of modules of Walsh coefficients of Boolean functions
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

The sum of modules of Walsh coefficients of Boolean functions

  • Reynier A. de la Cruz Jimenez und Oleg V. Kamlovskiy EMAIL logo
Veröffentlicht/Copyright: 8. November 2016
Veröffentlichen auch Sie bei De Gruyter Brill
Informationen für Autor*innen Erkunden Sie dieses Fachgebiet
Discrete Mathematics and Applications
Aus der Zeitschrift Discrete Mathematics and Applications Band 26 Heft 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

[1] O. A. Logachev, A. A. Sal’nikov, S. V. Smyshlyaev, V. V. Yashchenko, Boolean functions in coding theory and cryptology, M.: MCCME, 2012 (in Russian), 584 pp.10.1515/dma-2012-022Suche in Google Scholar

[2] O. V. Kamlovskiy, “The number of occurrences of elements in the output sequences of filter generators”Prikladnaya diskretnaya matematika, 2013,. 3(21), 11–25 (in Russian).Suche in Google Scholar

[3] R.L. McFarland, “A family of difference sets in non-cyclic groups”J. Comb. Theory. Ser. A, 15: 1 (1973), 1–10.10.1016/0097-3165(73)90031-9Suche in Google Scholar

[4] C. Carlet, “A large class of cryptographic Boolean functions via a study of the Maiorana-McFarland construction”Lect. Notes Comput. Sci., 2442 (2002), 549–564.10.1007/3-540-45708-9_35Suche in Google Scholar

[5] H. Dobbertin, “Construction of bent functions and balanced Boolean functions with high nonlinearity”, Lect. Notes Comput. Sci., 1008 (1995), 61–74.10.1007/3-540-60590-8_5Suche in Google Scholar

[6] M. M. Glukhov, V. P. Elizarov, A. A. Nechaev, Algebra: Textbook, II, M.: Gelios ARV, 2003 (in Russian), 416 pp.Suche in Google Scholar

[7] J. Riordan, Combinatorial Identities, Wiley, New York, 1968.Suche in Google Scholar

[8] R.A. Rueppel, Analysis and design of stream ciphers, Springer-Verlag, 1986, 244 pp.10.1007/978-3-642-82865-2Suche in Google Scholar

[9] C. Carlet, “Boolean functions for cryptography and error correcting codes”Boolean Models and Methods in Mathematics, Computer Science, and Engineering, eds. Y. Crama, P. L. Hammer, Cambridge Univ. Press, 2010, 257–397.10.1017/CBO9780511780448.011Suche in Google Scholar

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

© 2016 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  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
https://doi.org/10.1515/dma-2016-0023
Schlagwörter für diesen Artikel
Boolean functions; Walsh coefficients; filtering generators

Artikel in diesem Heft

  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
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2025 De Gruyter Brill
Heruntergeladen am 1.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/dma-2016-0023/html?lang=de
Button zum nach oben scrollen