Skip to main content
Log in

Abelian difference sets with multiplier minus one

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. T.Beth, D.Jungnickel and H.Lenz, Design Theory. London-New York 1986.

  2. D. Ghinelli-Smit, A new result on difference sets with −1 as multiplier. Geom. Dedicata23, 309–317 (1987).

    Google Scholar 

  3. D. R.Hughes, I H.Van Lint and R. M.Wilson, Announcement at the 7th British Combinatorial Conference. Cambridge 1979.

  4. E. C. Johnsen, The inverse multiplier for abelian group difference sets. Canad. J. Math.16, 787–796 (1964).

    Google Scholar 

  5. D. Jungnickel, Difference sets with multiplier −1. Arch. Math.38, 511–513 (1982).

    Google Scholar 

  6. E. S.Lander, Symmetric Designs: An Algebraic Approach. London-New York 1983.

  7. E. S.Lander, Topics in Algebraic Coding Theory. D. Phil. Thesis, Oxford Univ. 1980.

  8. S. L.Ma, On association schemes, Schur rings, strongly regular graphs and partial difference sets. Ars Combin., to appear.

  9. S. L.Ma, Polynomial Addition Sets and Symmetric Difference Sets. Research Report347, National University of Singapore 1988.

  10. S. L.Ma, A family of difference sets having −1 as an invariant. Europ. J. Combin., to appear.

  11. H. B.Mann, Addition Theorems. New York 1965.

  12. H. B. Mann andR. L. Mc.Farland, On multipliers of difference sets. Canad. J. Math.17, 541–542 (1965).

    Google Scholar 

  13. R. L.McFarland, Sub-difference sets of Hadamard difference sets. J. Combin. Theory Ser. A, to appear.

  14. R. L. McFarland, A family of difference sets in non-cyclic groups. J. Combin. Theory Ser. A15, 1–10 (1973).

    Google Scholar 

  15. R. L. McFarland andB. F. Rice, Translates and multipliers of abelian difference sets. Proc. Amer. Math. Soc.68, 375–379 (1978).

    Google Scholar 

  16. P. K. Menon, On difference sets Whose parameters satisfy a certain relation. Proc. Amer. Math. Soc.13, 739–745 (1962).

    Google Scholar 

  17. M. Miyamoto, A family of difference sets having −1 as an invariant. Hokkaido Math. J.12, 24–26 (1983).

    Google Scholar 

  18. A. Pott, On abelian difference sets with multiplier −1. Arch Math.53, 510–512 (1989).

    Google Scholar 

  19. I.Schur, Zur Theorie der einfach transitiven Permutationsgruppen. S. B. Preuss. Akad. Wiss. Phys.-Math. Kl. 598–623 (dy1933).

  20. R. J. Turyn, A special class of Williamson matrices and difference sets. J. Combin. Theory Ser. A36, 111–115 (1984).

    Google Scholar 

  21. H.Wielandt, Finite Permutation Groups. New York-London 1964.

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was performed in part while the authors attended Workshops on Design Theory and Coding Theory at the Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, Minnesota, June 1988. The authors were partially supported at the Institute with funds provided by the National Science Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

McFarland, R.L., Ma, S.L. Abelian difference sets with multiplier minus one. Arch. Math 54, 610–623 (1990). https://doi.org/10.1007/BF01188691

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01188691

Navigation