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Orbital derivatives over subgroups and their combinatorial and group-theoretic properties

  • Boris A Pogorelov EMAIL logo and Marina A Pudovkina
Published/Copyright: November 14, 2016
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Discrete Mathematics and Applications
From the journal Discrete Mathematics and Applications Volume 26 Issue 5

Abstract

Properties of the orbital derivatives over subgroups of the group Gn generated by the additive groups of the residue ring š•«2n and the n-dimensional vector space Vn over the field GF(2) are considered. Nonrefinable sequences of nested orbits for the subgroups of the group Gn and of the Sylow subgroup Pn of the symmetric group S2n are described. For the orbital derivatives, three analogs of the concept of the degree of nonlinearity for functions over š•«2n or Vn are suggested.

Keywords: additive group of the residue ring; additive group of the vector space; Sylow 2-subgroup; degree of nonlinearity; normal subgroups

References

[1] Discrete mathematics. Encyclopaedia., M.: Nauchnoe izdatelā€™stvo Ā«Bolā€™shaya Rossiyskaya entsiklopediyaĀ», 2004 (in Russian).Search in Google Scholar

[2] Cusick T. W., Stănică P., Cryptographic Boolean Functions and Applications, Elsevier, 2009, 232 pp.10.1016/B978-0-12-374890-4.00009-4Search in Google Scholar

[3] Pogorelov B. A., Pudovkina M. A., ā€œOrbital derivatives on residue rings. Part I. General propertiesā€, Mat. Vopr. Kriptogr., 5:4 (2014), 99-127 (in Russian).10.4213/mvk137Search in Google Scholar

[4] Pogorelov B. A., Pudovkina M. A., ā€œOrbital derivatives on the residue ring. Part II. Probabilistic and combinatorial propertiesā€, Mat. Vopr. Kriptogr., 6:1 (2015), 117-133 (in Russian).10.4213/mvk154Search in Google Scholar

[5] Pogorelov B. A., Pudovkina M. A., ā€œOrbital derivatives and supergroups of regular additive groupsā€, Mat. Vopr. Kriptogr., 2016 (to appear) (in Russian).Search in Google Scholar

[6] Sachkov V. N., Introduction to the combinatorial methods of discrete mathematics, M: MCCME, 2004 (in Russian).Search in Google Scholar

[7] Cheremushkin A. V., ā€œThe additive approach to the determination of the nonlinear degree of a discrete functionā€, Prikl. Diskr. Mat., 2010, No.2, 22-33 (in Russian).10.17223/20710410/8/4Search in Google Scholar

[8] Cheremushkin A. V., ā€œThe additive approach to the determination of the nonlinear degree of a discrete function on cyclic group of prime orderā€, Prikl. Diskr. Mat., 2013,.2, 26-38 (in Russian).10.17223/20710410/20/4Search in Google Scholar

[9] Cheremushkin A. V., ā€œComputation of the degree of a nonlinear function on cyclic group of prime orderā€, Prikl. Diskr. Mat., 2014,.2, 37-47 (in Russian).10.17223/20710410/24/4Search in Google Scholar

Received: 2014-12-26
Published Online: 2016-11-14
Published in Print: 2016-10-1

Ā© 2016 Diogenes Co., Sofia

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https://doi.org/10.1515/dma-2016-0026
Keywords for this article
additive group of the residue ring; additive group of the vector space; Sylow 2-subgroup; degree of nonlinearity; normal subgroups

Articles in the same Issue

  1. Frontmatter
  2. Research Article
  3. A generalization of Oreā€™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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