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Dergiler / 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
Sayfa
139–148
Yayın Tarihi
2021-05-20
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

🎯
Amaç & Hipotez:We provide some applications of a polynomial criterion for difference sets.
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Temel Bulgular & Veri:These include counting the difference sets with specified parameters in terms of Hilbert functions, in particular a count of bent functions.
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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.

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Bu Makaleye Atıf Yap

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

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Kaynakça (10)

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  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).