Corpus ID: 117988705

An Investigation of Group Developed Weighing Matrices

@inproceedings{Hollon2010AnIO,
  title={An Investigation of Group Developed Weighing Matrices},
  author={J. Hollon},
  year={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 are 1, 0 or -1 and has the property that the matrix times its transpose is some integer multiple of the identity matrix. We examine the case where these matrices are said to be developed by an abelian group. Through a combination of extending previous results and by giving explicit constructions we… Expand
1 Citations
Cohomology Developed Matrices - constructing weighing matrices from their automorphisms
The aim of this work is to construct families of weighing matrices via automorphisms and cohomology. We study some well known families such as Payley's conference and Hadamard matrices and ProjectiveExpand

References

SHOWING 1-10 OF 21 REFERENCES
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
Circulant weighing designs
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 circulantExpand
Hadamard matrices of order 764 exist
TLDR
Two Hadamard matrices of order 764 of Goethals– Seidel type are constructed and it is shown that among the remaining 14 integers n only four are less than 1000, and the revised list now includes these four integers. Expand
On circulant and two-circulant weighing matrices
TLDR
New weighing matrices are constructed which are listed as open in the second edition of the Handbook of Combinatorial Designs and fill a missing entry in Strassler’s table with answer “YES”. Expand
A note on balanced weighing matrices
A balanced weighing matrix is a square orthogonal matrix of 0’s, 1’s and −1’s such that the matrix obtained by squaring entries is the incidence matrix of a (v, k, λ) configuration. Properties ofExpand
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
Perfect Ternary Arrays
A perfect ternary array is an r-dimensional array with entries 0, +1 and —1 such that all of its out-of-phase periodic autocorrelation coefficients are zero. Such an array is equivalent to a groupExpand
Circulant weighing matrices
TLDR
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
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
Determination of all possible orders of weight 16 circulant weighing matrices
We show that a circulant weighing matrix of order n and weight 16 exists if and only if n>=21 and n is a multiple of 14,21 or 31.
...
1
2
3
...