Some results on weighing matrices

  title={Some results on weighing matrices},
  author={Jennifer Wallis and A. Whiteman},
  journal={Bulletin of The Australian Mathematical Society},
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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Some Nonexistence and Asymptotic Existence Results for Weighing Matrices
Orthogonal designs and weighing matrices have many applications in areas such as coding theory, cryptography, wireless networking, and communication. In this paper, we first show that if positiveExpand
Structure of group invariant weighing matrices of small weight
Abstract We show that every weighing matrix of weight n invariant under a finite abelian group G can be generated from a subgroup H of G with | H | ≤ 2 n − 1 . Furthermore, if n is an odd prime powerExpand
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The results fill in 52 missing entries in Strassler’s table of circulant weighing matrices (Strassler 1997), which considers matrices of order 1–200 with weight k ≤ 100. Expand
New circulant weighing matrices of prime order in CW(31,16), CW(71,25), CW(127,64)
Abstract Adapting the P. Eades conjecture about the existence of a multiplier for every (v,k,μ)-design to the more specific circulant weighing matrices in CW(p,s2) for a prime number p, we are ableExpand
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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
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
  • 1974