Circulant weighing designs

@article{Arasu1996CirculantWD,
  title={Circulant weighing designs},
  author={K. T. Arasu and Jennifer Seberry},
  journal={Journal of Combinatorial Designs},
  year={1996},
  volume={4},
  pages={439-447}
}
Algebraic techniques are employed to obtain necessary conditions for the existence of certain families of circulant weighing designs. As an application we rule out the existence of many circulant weighing designs. In particular, we show that there does not exist a circulant weighing matrix of order 43 for any weight. We also prove two conjectures of Yosef Strassler. © 1996 John Wiley & Sons, Inc. Disciplines Physical Sciences and Mathematics Publication Details Arasu K T and Seberry J… Expand
An Investigation of Group Developed Weighing Matrices
Hollon, Je R. M.S., Department of Mathematics and Statistics, Wright State University, 2010. An Investigation of Group Developed Weighing Matrices. A weighing matrix is a square matrix whose entriesExpand
Some New Results on Circulant Weighing Matrices
We obtain a few structural theorems for circulant weighing matrices whose weight is the square of a prime number. Our results provide new schemes to search for these objects. We also establish theExpand
New weighing matrices and orthogonal designs constructed using two sequences with zero autocorrelation function – a review
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
The Classification of Circulant Weighing Matrices of Weight 16 and Odd Order
In this paper we completely classify the circulant weighing matrices of weight 16 and odd order. It turns out that the order must be an odd multiple of either 21 or 31. Up to equivalence, there areExpand
When the necessary conditions are not sufficient: sequences with zero autocorrelation function
Recently K. T. Arasu (personal communication) and Yoseph Strassler, in his PhD thesis, The Classification of Circulant Weighing Matrices of Weight 9, Bar-Ilan University, Ramat-Gan, 1997, haveExpand
Group developed weighing matrices
TLDR
The question of existence for 318 weighing matrices of order and weight both below 100 is answered, and some of the new results provide insight into the existence of matrices with larger weights and orders. Expand
Study of proper circulant weighing matrices with weight 9
TLDR
The first theoretical proof of the spectrum of orders n for which circulant weighing matrices with weight 9 exist is provided, which consists of those positive integers n, which are multiples of 13 or 24. Expand
Symmetric Weighing Matrices Constructed using Group Matrices
TLDR
It is proved that there is no symmetric abelian group weighing matrices of order 2pr and weight p2 where p is a prime and p≥ 5. Expand
Circulant weighing matrices of weight 22t
TLDR
A complete computer search is made for all circulant weighing matrices of order 16 such that MMT = kIn for some positive integer t and new structural results are obtained. Expand
A reduction theorem for circulant weighing matrices
  • K. Arasu
  • Computer Science, Mathematics
  • Australas. J Comb.
  • 1998
TLDR
The results establish the nonexistence of WC(n, k) for the pairs (n,k) = (125,25), (44,36), (64, 36), (66,36) and (80,36). Expand
...
1
2
...

References

SHOWING 1-10 OF 13 REFERENCES
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
Some results on weighing matrices
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
On the existence of orthogonal designs
An orthogonal design of type (s^, s ^ , s^) and order n on the comniuting variables x , x , x , is an n n matrix A with entries -L ^ Z't from {o, ir^, such that = V 2 ) S .X . ^=l I . The existenceExpand
Relative difference sets with n = 2
TLDR
The results give strong evidence for the following conjecture : the only non-trivial difference sets which admit extensions to relative difference sets with n = 2 have the parameters of the complements of Singer difference set with even dimension. Expand
Polynomial addition sets and polynomial digraphs
Abstract Let G be a group of order v , and f ( x ) be a nonzero integral polynomial. A ( v, k, f ( x ))-polynomial addition set in G is a subset D of G with k distinct elements such that f (Σ d ∈ D dExpand
The Solution of the Waterloo Problem
TLDR
Those Singer difference sets D(d, q) which admit a “Waterloo decomposition” D = A ∪ B such that (A − B) · (A + B)(−1) = k in Z G are characterized. Expand
Circulant weighing matrices
CHAPTER I HISTORY AND APPLICATIONS ........................... 1 CHAPTER II BASIC PROPERTIES ................................... 8 A Geometric Visualisation .......................... 14 EquivalenceExpand
Orthogonal Designs: Quadratic Forms and Hadamard Matrices
Multiplier theorem for a difference list
  • Ars Combin .
  • 1977
...
1
2
...