# Orthogonal Designs IV: Existence Questions

```@article{Geramita1975OrthogonalDI,
title={Orthogonal Designs IV: Existence Questions},
author={Anthony V. Geramita and Jennifer Seberry},
journal={J. Comb. Theory, Ser. A},
year={1975},
volume={19},
pages={66-83}
}```
• Published 1975
• Computer Science, Mathematics
• J. Comb. Theory, Ser. A
In  Raghavarao showed that if n = 2 (mod 4) and A is a {O, 1, -1} matrix satisfying AAt = (n 1) In. then n 1 = a2 b2 for a, b integers. In  van Lint and Seidel giving a proof modeled on a proof of the Witt cancellation theorem, proved more generally that if n is as above and A is a rational matrix satisfying AAt = kIn then k = q12 + q22 (q1, q2 E Q, the rational numbers). Consequently, if k is an integer then k = a2 + b2 for two integers a and b. In  we showed that if, in addition, A… Expand
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• Mathematics
• 1976
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• Mathematics
• 1975
It is shown that if q is a prime power then there exists a circulant weighing matrix of order q 2 + q + 1 with q 2 nonzero elements per row and column. This result allows the bound N to be lowered inExpand
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• Mathematics
• 1999
Abstract The book, Orthogonal Designs : Quadratic Forms and Hadamard Matrices , Marcel Dekker, New York-Basel, 1979, by A.V. Geramita and Jennifer Seberry, has now been out of print for almost twoExpand
On sufficient conditions for some orthogonal designs and sequences with zero autocorrelation function
• Computer Science
• Australas. J Comb.
• 1996
We give new sets of sequences with entries from {0, ±a, ±b, ±c, ±d} on the commuting variables a, b, c, d and zero autocorrelation function. Then we use these sequences to construct some newExpand
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• Mathematics
• 1993
We give new sets of {0, 1, -1} sequences with zero autocorrelation function, new constructions for weighing matrices and review the weighing matrix conjecture for orders 4t, t є {1,...,25}Expand
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Real orthogonal designs were first introduced in the 1970’s, followed shortly by the introduction of complex orthogonal designs. These designs can be described simply as square matrices whose columnsExpand
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• 1974
This paper surveys orthogonal designs which are an overview of Baumert-Hall arrays, Hadamard matrices and weighing matrices. The known results are given and unsolved problems indicated. DisciplinesExpand
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• Computer Science, Mathematics
• Australas. J Comb.
• 1993
The skew weighing matrix conjecture for orders 2t is verified, proving the conjecture for t ≥ 3.13, t ≥ 5, and new results for 2t.15 are given. Expand