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An Asymptotic Existence Result for Orthogonal Designs

  • Hadi Kharaghani
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 329)

Abstract

Orthogonal matrices with indeterminate entries are called orthogonal designs. There is a strong relationship between orthogonal designs and quadratic forms. Orthogonal designs are used to construct Hadamard matrices and, more generally, weighing matrices. Despite the importance of orthogonal designs, not much is known about their existence or construction. We use a powerful new constructive technique to find a kind of asymptotic existence result for orthogonal designs.

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References

  1. [1]
    R. Craigen, “Signed groups, sequences and asymptotic existence of Hadamard matrices”, to appear in JCT.Google Scholar
  2. [2]
    R. Craigen, W.H. Holzmann, and H. Kharaghani, “On the asymptotic existence of Complex Hadamard matrices”, preprint 1994.Google Scholar
  3. [3]
    A. Geramita and J. Seberry, Quadratic Forms, Orthogonal Designs, and Hadamard Matrices, Vol. 45 of Lecture Notes in Pure and Applied Mathematics, Marcel Dekker Inc., New York and Basel, 1979.Google Scholar
  4. [4]
    W. Wolfe, “Amicable orthogonal designs–existence”, Can. J. Math, 28 (1976), pp. 1006–1020.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Hadi Kharaghani
    • 1
    • 2
  1. 1.Dept. of Mathematics & Computer ScienceUniversity of LethbridgeLethbridgeUSA
  2. 2.Institute for Studies in Theoretical Physics and MathematicsTehranIran

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