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Reversible relative difference sets

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Abstract

We investigate nontrivial (m, n, k, λ)-relative difference sets fixed by the inverse. Examples and necessary conditions on the existence of relative difference sets of this type are studied.

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References

  1. K. T. Arasu, D. Jungnickel andA. Pott: Divisible Difference Sets with Multiplier-1,J. Algebra 133 (1990), 35–62.

    Google Scholar 

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

    Google Scholar 

  3. A. T. Butson: Generalized Hadamard Matrices,Proc. Amer. Math. Soc. 13 (1962), 894–898.

    Google Scholar 

  4. A. T. Butson: Relations Among Generalized Hadamard Matrices, Relative Difference Sets, and Maximal Length Linear Recurring Sequences,Can. J. Math. 15 (1963), 42–48.

    Google Scholar 

  5. J. F. Dillon: Difference Sets in 2-groups,Proc. NSA Math. Sc. Meeting (1987), 165–172.

  6. J. E. H. Elliott andA. T. Butson: Relative Difference Sets,Illinois J. Math. 10 (1966), 517–531.

    Google Scholar 

  7. M. Hall, Jr.:The Theory of Groups, Chelsea Publishing Company, New York, 1976.

    Google Scholar 

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

    Google Scholar 

  9. K. H. Leung andS. L. Ma: Construction of Partial Difference Sets and Relative Difference Sets onp-groups,Bull. London Math. Soc. 22 (1990), 533–539.

    Google Scholar 

  10. S. L. Ma: On Association Schemes, Schur Rings, Strongly Regular Graphs and Partial Difference Sets,Ars Combinatoria 27 (1989), 211–220.

    Google Scholar 

  11. R. L. McFarland: Sub-Difference Sets of Hadamard Difference Sets,J. Combin. Th. Ser. A. 54 (1990), 112–122.

    Google Scholar 

  12. P. K. Menon: On Difference Sets whose Parameters Satisfy a Certain Relation,Proc. Amer. Math. Soc. 13 (1962), 739–745.

    Google Scholar 

  13. J-P. Serre:Linear Representations of Finite Groups, Springer, New York, 1978.

    Google Scholar 

  14. R. J. Turyn: A Special Class of Williamson Matrices and Difference Sets,J. Combin. Th. Ser. A 36 (1984), 111–115.

    Google Scholar 

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Authors and Affiliations

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

    S. L. Ma

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  1. S. L. Ma
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Ma, S.L. Reversible relative difference sets. Combinatorica 12, 425–432 (1992). https://doi.org/10.1007/BF01305235

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  • DOI: https://doi.org/10.1007/BF01305235

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