# 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

#### 17 Citations

An Investigation of Group Developed Weighing Matrices

- Mathematics
- 2010

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 entries… Expand

Some New Results on Circulant Weighing Matrices

- Mathematics
- 2001

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 the… Expand

New weighing matrices and orthogonal designs constructed using two sequences with zero autocorrelation function – a review

- 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 two… Expand

The Classification of Circulant Weighing Matrices of Weight 16 and Odd Order

- Mathematics
- 1999

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 are… Expand

When the necessary conditions are not sufficient: sequences with zero autocorrelation function

- Mathematics
- 1999

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, have… Expand

Group developed weighing matrices

- Computer Science, Mathematics
- Australas. J Comb.
- 2013

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

- Computer Science, Mathematics
- Discret. Math.
- 2008

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

- Mathematics, Computer Science
- Des. Codes Cryptogr.
- 2005

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

- Computer Science, Mathematics
- Des. Codes Cryptogr.
- 2006

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

- Computer Science, Mathematics
- Australas. J Comb.
- 1998

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

#### References

SHOWING 1-10 OF 13 REFERENCES

New circulant weighing matrices of prime order in CW(31,16), CW(71,25), CW(127,64)

- Mathematics
- 1998

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 able… Expand

Some results on weighing matrices

- 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 in… Expand

On the existence of orthogonal designs

- Mathematics
- 1978

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 existence… Expand

Relative difference sets with n = 2

- Computer Science, Mathematics
- Discret. Math.
- 1995

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

- Mathematics
- 1985

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 d… Expand

The Solution of the Waterloo Problem

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 1995

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

- Mathematics
- 1977

CHAPTER I HISTORY AND APPLICATIONS ........................... 1 CHAPTER II BASIC PROPERTIES ................................... 8 A Geometric Visualisation .......................... 14 Equivalence… Expand

Multiplier theorem for a difference list

- Ars Combin .
- 1977