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Difference sets in dihedral groups

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Abstract

We study the existence of nontrivial (2m, k, λ)-difference sets in dihedral groups. Some nonexistence results are proved. In particular, we show that n = k − λ is odd and ϕ(n)/n < 1/2. Finally, a computer search shows that, except 5 undecided cases, no nontrivial difference set exists in dihedral groups for n ≤ 106.

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References

  • Baumert, L.D. 1971. Cyclic Difference Sets. New York: Springer-Verlag.

    Google Scholar 

  • Beth, T., Jungnickel, D., and Lenz, H. 1986. Design Theory. Cambridge: Cambridge University Press.

    Google Scholar 

  • Fan, C.T., Siu, M.K., and Ma, S.L. 1985. Difference Sets in dihedral groups and interlocking difference sets. Ars Combinatoria, 20A:99–107.

    Google Scholar 

  • Lander, E.S., 1983. Symmetric Designs: An Algebraic Approach, Cambridge: Cambridge University Press.

    Google Scholar 

  • Ma, S.L. 1984. On rational circulants satisfying A m = dl + λ J. Linear Algebra Appl, 62:155–161.

    Google Scholar 

  • McFarland, R.L. and Ma, S.L. 1990. Abelian difference sets with multiplier minus one. Arch. Math., 54:610–623.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 0511, Singapore, Singapore

    Ka Hin Leung, Siu Lun Ma & Yan Loi Wong

Authors
  1. Ka Hin Leung
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  2. Siu Lun Ma
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  3. Yan Loi Wong
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Communicated by D. Jungnickel

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Leung, K.H., Ma, S.L. & Wong, Y.L. Difference sets in dihedral groups. Des Codes Crypt 1, 333–338 (1991). https://doi.org/10.1007/BF00124608

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  • DOI: https://doi.org/10.1007/BF00124608

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