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
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References
Peter Eades, "Some asymptotic existence results for orthogonal designs", Ars. Combinatoria.
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Jennifer Seberry Wallis, "Orthogonal designs V: orders divisible by eight", Utilitas Math. 9 (1976), 263–281.
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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
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