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Quadruple systems over Zp admitting the affine group

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Combinatorial Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 969))

Abstract

A necessary and sufficient condition for the existence of t-(p,k,λ) designs which are invariant under the affine group Ap={x → ax+b : a,b ε GF(p), a ≠ 0} is given. From this we derive sufficient criteria für the existence of Ap-invariant 3-(p,4,λ) designs for all primes p. These designs are simple in the case p ≡ 5(mod 12) and λ=2. As a corollary to our considerations, we obtain some infinite series of simple 2-(p,r,λ) designs for all primes p and certain values of λ which are also invariant under Ap.

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References

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Authors and Affiliations

  1. Mathematisches Seminar der Universität Hamburg, 2000, Hamburg 12, Federal Republic of Germany

    Egmont Köhler

Authors
  1. Egmont Köhler
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Dieter Jungnickel Klaus Vedder

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© 1982 Springer-Verlag

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Köhler, E. (1982). Quadruple systems over Zp admitting the affine group. In: Jungnickel, D., Vedder, K. (eds) Combinatorial Theory. Lecture Notes in Mathematics, vol 969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062996

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  • DOI: https://doi.org/10.1007/BFb0062996

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11971-5

  • Online ISBN: 978-3-540-39380-1

  • eBook Packages: Springer Book Archive

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