Some results on weighing matrices

@article{Wallis1975SomeRO,
  title={Some results on weighing matrices},
  author={Jennifer Wallis and A. Whiteman},
  journal={Bulletin of The Australian Mathematical Society},
  year={1975},
  volume={12},
  pages={433-447}
}
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 in the theorem of Geramita and Wallis that “given a square integer k there exists an integer N dependent on k such that weighing matrices of weight k and order n and orthogonal designs (1, k ) of order 2 n exist for every n > N ”. 
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References

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Families of weighing matrices
A weighing matrix is an n × n matrix W = W ( n , k ) with entries from {0, 1, −1}, satisfying = WW t = KI n . We shall call k the degree of W . It has been conjectured that if n ≡ 0 (mod 4) thenExpand
Orthogonal designs III: Weighing matrices
A weighing matrix W = W(n,k) of order n and weight k is a square (0,l,-l)-matrix satisfying WWt -kIn An orthogonal design of order n on a single variable is a weighing matrix and consequently theExpand
Orthogonal Designs IV: Existence Questions
In [5] 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 [4] van Lint and Seidel giving a proof modeled on a proofExpand
Orthogonal designs II
AbstractOrthogonal designs are a natural generalization of the Baumert-Hall arrays which have been used to construct Hadamard matrices. We continue our investigation of these designs and show thatExpand
Skew Hadamard matrices of Goethals-Seidel type
TLDR
The main result states that if q is a prime power = 3(mod 8), then there exists a skew Hadamard matrix of order 4n = q + 1 that is of the Goethals-Seidel type. Expand
Variants of cyclic difference sets
Received by the editors February 20, 1973. AMS (MOS) subject classifications (1970). Primary 05B10, 05B20, 05B25; Secondary 05B05, 15A24.
, and Jennifer S . Wallis , " Families of weighing matrices "
  • Bull . Austral . Math . Soc .
  • 1974
Geramita and Jennifer Seberry Wall is , " Orthogonal designs III : weighing matrices "
  • UtiUtas Math .
  • 1974
Seberry Wall is, "Orthogonal designs III: weighing matrices
  • UtiUtas Math
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