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Necessary conditions for menon difference sets

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Abstract

Menon difference sets have the parameters (4N 2, 2N 2±N,N 2±N). In this paper, a necessary condition for Menon difference sets in groups of the formZ 2p ×Z 2p ×G q , whereG q is an abelianq-group andp, q are distinct prime numbers, will be proved. We will also focus on the groupsZ 2pq ×Z 2pq and give constraints on the magnitudes ofp andq. Finally, we show that if the groupZ 6p ×Z 6p contains a Menon difference set, thenp=3 or 13 only.

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References

  1. Arasu, K.T., Davis, J.A., Jedwab, J., and Sehgal, S.K. New constructions of Menon difference sets,submitted.

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

    Google Scholar 

  3. Chan, W.K. 1991. Perfect arrays and menon difference sets. M. Phil. Thesis, University of Hong Kong.

  4. Chan, W.K., Siu, M.K. and Ma, S.L. Non-existence of Certain Perfect arrays. To appear inDisc. Math.

  5. Dillon, J.F. 1987. Difference sets in 2-groups. InProc. NSA Math. Sci. Meetings, pp. 165–172.

  6. Davis, J.A. 1987. Difference sets in Abelian 2-Groups. Ph.D. Thesis, University of Virginia.

  7. Jedwab, J. 1992. Generalized perfect arrays and Menon difference sets.Designs, Codes and Cryptography, 2:19–68.

    Google Scholar 

  8. Jedwab, J., Mitchell, C.J., Piper, F., and Wild, P. Perfect arrays and difference sets. To appear inDisc. Math.

  9. Jungnickel, D. 1989. Design theory: An update.Ars Combinatorica, 28:129–199.

    Google Scholar 

  10. McFarland, R.L. 1989. Difference sets in abelian group of order 4 p 2.Mitt. Math. Sem., Giessen, 192:1–70.

    Google Scholar 

  11. Menon, P.K. 1962. On difference sets whose parameters satisfy a certain relation.Proc. Amer. Math. Soc., 13:739–745.

    Google Scholar 

  12. Storer, T. 1967.Cyclotomy and difference sets, Chicago: Markham Publishing Company.

    Google Scholar 

  13. Turyn, R.J. 1965. Character sums and difference sets.Pacific J. Math 15:319–346.

    Google Scholar 

  14. Turyn, R.J. 1984. A special class of Williamson matrices and difference sets.J. Comb. Th (A), 36:111–115.

    Google Scholar 

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Authors and Affiliations

  1. The Ohio State University, 43210, Columbus, OH

    W. K. Chan

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  1. W. K. Chan
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Communicated by R. Mullin

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Chan, W.K. Necessary conditions for menon difference sets. Des Codes Crypt 3, 147–154 (1993). https://doi.org/10.1007/BF01388413

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  • DOI: https://doi.org/10.1007/BF01388413

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