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A note on asymptotic existence results for orthogonal designs

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Part of the Lecture Notes in Mathematics book series (LNM,volume 622)

Abstract

In a recent manuscript "Some asymptotic results for orthogonal designs" Peter Eades showed that for many types of orthogonal designs existence is established once the order is large enough.

This paper uses sequences with zero non-periodic and periodic autocorrelation function to establish the asymptotic existence of many orthogonal designs with four variables. Bounds are also established for orthogonal designs of type (1, k) where k≤63 and (l) where l≤52.

It is shown that any 4 sequences with zero non-periodic auto-correlation function and 8k−1 entries +1 or −1 must have length at least 2k+1.

Keywords

  • Combinatorial Theory
  • Orthogonal Design
  • Circulant Matrice
  • Utilitas Math
  • Devious Method

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. Peter Eades, "Some asymptotic existence results for orthogonal designs", Ars. Combinatoria.

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  2. Peter Eades and Jennifer Seberry Wallis, "Some asymptotic results for orthogonal designs: II", Colloque sur Problèmes Combinatoires et Theorie des Graphes, Orsay, France, 1976.

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  3. Anthony V. Geramita, Joan Murphy Geramita, Jennifer Seberry Wallis, "Orthogonal designs", Linear and Multilinear Algebra 3 (1975/76), 281–306.

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© 1977 Springer-Verlag

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Eades, P., Wallis, J.S., Wormald, N. (1977). A note on asymptotic existence results for orthogonal designs. In: Little, C.H.C. (eds) Combinatorial Mathematics V. Lecture Notes in Mathematics, vol 622. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069183

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  • DOI: https://doi.org/10.1007/BFb0069183

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08524-9

  • Online ISBN: 978-3-540-37020-8

  • eBook Packages: Springer Book Archive