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On (p2, p, p2, p)-Difference Sets in ℤ3p

  • Yutaka Hiramine
Article

Abstract

In this article we consider (p2, p, p2, p)-Difference Sets in Z3p. Several classes of such difference sets are known. We classify these classes into two typical types and characterize them.

05B10 

Keywords

semiregular relative difference Sets planar functions group rings elementary abelian p-groups 

References

  1. Davis, J. A. 1991. A note on products of relative difference sets. Designs Codes Cryptogr., 1, 117–119.MathSciNetCrossRefGoogle Scholar
  2. Davis, J. A. 1992. Construction of relative difference sets in p-groups. Discrete Math., 103, 7–15.MathSciNetCrossRefGoogle Scholar
  3. Feng, T. 2007. Relative (pa, pb, pa, pab) difference sets in subgroups of sl(n, k). Finite Fields and Their Applications, 13, 769–772.MathSciNetCrossRefGoogle Scholar
  4. Gluck, D. 1990. A note on permutation polynomials and finite geometries. Discrete Math., 80, 97–100.MathSciNetCrossRefGoogle Scholar
  5. Hiramine, Y. 1989. A conjecture on affine planres of prime order. JCTA, 52, 44–50.CrossRefGoogle Scholar
  6. Ma, S. L., and A. Pott. 1995. Relative difference sets, planar functions, and generalized hadamard matrices. J. Algebra, 175, 505–525.MathSciNetCrossRefGoogle Scholar
  7. Pott, A. 1995. Finite geometry and character theory. In Lecture Notes in Mathematics, vol. 1601. Berlin, Springer-Verlag.Google Scholar
  8. Pott, A. 1996. Groups, difference sets and the monster. Ohio State University Mathematical Research Institute Publications, vol. 4, 195–232. Berlin–New York, Walter De Gruyter, Inc.Google Scholar
  9. Rónayi, L., and T. Szönyi. 1989. Planar functions over finite fields. Combintorica, 9, 315–320.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of EducationKumamoto UniversityKumamotoJapan

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