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Construction of Designs

  • Marshall HallJr.
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 20)

Abstract

Gold is where you find it. The same is true of designs. There are many ways to construct designs all of which work some of the time. The most valuable tool is a group G of automorphisms. If the order of G is large this can make the construction easy. We can start with some part of the incidence matrix, say rows or columns, or with a subdesign.

Keywords

Binary Code Triple System Incidence Matrix Projection Matrix Steiner Triple System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    M. Hall Jr., R. Roth, G.H. John van Rees, and S.A. Vanstone, “On Designs (22,23,12,8,4)”, J. Conbinatorial Theory (Series A) 47 (1988), 157–175.zbMATHCrossRefGoogle Scholar
  2. [2]
    N. Hamada and Y. Kobayashi, “On the block structure of BIB designs with parameters v = 22, b = 33, r = 12, k = 8 and λ = 4”, J. Combinatorial Theory (Series A) 24 (1978) 75–83.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    F.J. Mac Williams, N.J.A. Sloane, and J.G. Thompson, “On the existence of a projective plane of order 10”, J. Combinatorial Theory (Series A) 14 (1973) 66–78.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1990

Authors and Affiliations

  • Marshall HallJr.
    • 1
  1. 1.Department of MathematicsEmory UniversityAtlantaUSA

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