SavedAdd your journal

Journals / Journal of Algebra Combinatorics Discrete Structures and Applications / 2021 / Cilt: 8 - Sayı: 2

Algebraic methods in difference sets and bent functions

Pradipkumar H. KESKAR
Priyanka KUMARİ
Pages
139–148
Publication Date
2021-05-20
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also consider the question about the bentness of certain Boolean functions introduced by Carlet when the $\mathcal{C}$-condition introduced by him doesn't hold.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We provide some applications of a polynomial criterion for difference sets.
📊
Key Findings & Data:These include counting the difference sets with specified parameters in terms of Hilbert functions, in particular a count of bent functions.
💡
Conclusion & Impact:We also consider the question about the bentness of certain Boolean functions introduced by Carlet when the $\mathcal{C}$-condition introduced by him doesn't hold.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hilbert functions · $\mathcal{C}$-condition · Flat

Abstract

We provide some applications of a polynomial criterion for difference sets. These include counting the difference sets with specified parameters in terms of Hilbert functions, in particular a count of bent functions. We also consider the question about the bentness of certain Boolean functions introduced by Carlet when the $\mathcal{C}$-condition introduced by him doesn't hold.

🔖

Cite This Article

KESKAR, P. H., KUMARİ, P. (2021). Algebraic methods in difference sets and bent functions. Journal of Algebra Combinatorics Discrete Structures and Applications, Cilt: 8 - Sayı: 2, 139–148. https://ajindex.com/articles/861501

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (10)

  1. T. Becker, V. Weispfennig, Groebner bases a computational approach to commutative algebra, Springer (1993)
  2. C. Carlet, Two new classes of bent functions, Advances in Cryptology-EUROCRYPT’93, LNCS vol 765 (Ed. T. Hellseth) Springer-Verlag (1994) 77–101
  3. D. Cox, J. Little, D. O’Shea, Ideals, varieties and algorithms, Springer Verlag, New York Inc (2007)
  4. J. F. Dillon, Elementary hadamard difference sets, Ph. D. Thesis, University of Maryland (1974)
  5. P. H. Keskar, P. Kumari, Polynomial criterion for abelian difference sets, Indian Journal of Pure and Applied Mathematics 51(1) (2020) 233–249
  6. N. Kolomeec, The graph of minimal distances of bent functions and its properties, Designs, Codes and Cryptography 85 (2017) 395–410
  7. B. Mandal, P. Stanica, S. Gangopadhyay, E. Pasalic, An analysis of the C class of bent functions, Fundamenta Informaticae 146(3) (2016) 271–292
  8. E. H. Moore, H. S. Pollatsek, Difference sets, connecting algebra, combinatorics, and geometry, american mathematical society (2013)
  9. N.Tokareva, Bent functions: Results and applications to cryptography, Elsevier (2015)
  10. A. van den Essen, Polynomial automorphisms and the jacobian conjecture, Birkhauser (2000).