Designs, Codes and Cryptography

, Volume 57, Issue 3, pp 373–381 | Cite as

Geometric and design-theoretic aspects of semibent functions I

Article

Abstract

The two parts of this paper consider combinatorial and geometric aspects of semibent functions. In the first part of this note we obtain 2-designs from semibent functions and we characterize their automorphism groups. In the second part semibent functions of partial spread type with a linear structure are investigated.

Keywords

Semibent function Design Automorphism group 

Mathematics Subject Classification (2000)

05B10 06E30 51E05 94B27 

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References

  1. 1.
    Arasu K.T., Dillon J.F.: Perfect Ternary Arrays, in Difference Sets, Sequences and their Correlation Properties (Bad Windsheim 1998), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., p 542, Kluwer, Dordrecht (1999).Google Scholar
  2. 2.
    Bending T.: Bent functions, SDP designs and their automorphism groups. Thesis, Queen Mary and Westfield College, University of London (1993).Google Scholar
  3. 3.
    Bernasconi A., Codenotti C.: Spectral analysis of boolean functions as a graph eigenvalue problem. IEEE Trans. Comput. 50, 984–985 (2001)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Canteaut A., Charpin P.: Decomposing bent functions. IEEE Trans. Inform. Theory 49, 2004–2019 (2003)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Chee S., Lee S., Kim K.: Semi-bent functions, LNCS 917, Advances in cryptology (ASIACRYPT-94), pp. 107–118. Springer (1994).Google Scholar
  6. 6.
    Dembowski P., Wagner A.: Some characterizations of finite projective spaces. Arch. Math. 11, 465–469 (1960)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Dillon J.: A survey of bent functions. NSA Tech. J. Special Issue, 191–215 (1972).Google Scholar
  8. 8.
    Dillon J.: Elementary hadamard difference sets, in Proceedings of 6th SE Conference on Combinatorics, Graph Theory and Computing, Utilitas Math., pp. 237–249. Boca Raton (1975).Google Scholar
  9. 9.
    Hou X.: Cubic bent functions. Discrete Math. 189, 149–161 (1998)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Kantor W.: Symplectic groups, symmetric designs and line ovals. J. Algebra 33, 43–58 (1975)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Kantor W: Exponential numbers of two weight codes, difference sets and symmetric designs. Discrete Math. 46, 95–98 (1983)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Mann B.: Difference sets in elementary abelian groups. Ill. J. Math. 9, 212–219 (1965)MATHGoogle Scholar
  13. 13.
    Neumann T.: Bent functions. Diploma Thesis, Universität Kaiserslautern (2006). http://www.mathematik.uni-kl.de/~dempw/Thesis.html.
  14. 14.
    Zheng Y., Zhang X.-M.: Relationships between bent functions and complementary plateaued functions, LNCS 1787, ICISC 99, pp. 60–75. Springer (1999).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.University of KaiserslauternKaiserslauternGermany

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