Corpus ID: 13953279

On the weighing matrices of order 4n and weight 4n-2 and 2n-1

@article{Gysin1995OnTW,
  title={On the weighing matrices of order 4n and weight 4n-2 and 2n-1},
  author={Marc Gysin and J. Seberry},
  journal={Australas. J Comb.},
  year={1995},
  volume={12},
  pages={157-174}
}
We give algorithms and constructions for mathematical and computer searches which allow us to establish the existence of W(4n, 4n - 2) and W (4n, 2n - 1) for many orders 4n less than 4000. We compare these results with the orders for which W(4n, 4n) and W(4n, 2n) are known. We use new algorithms based on the theory 

Tables and Topics from this paper

New D-optimal designs via cyclotomy and generalised cyclotomy
  • Marc Gysin
  • Mathematics, Computer Science
  • Australas. J Comb.
  • 1997
TLDR
D-optimal designs are given here for the first time, via computer-search, for v = ~ = 7,13,19,21,31,33,37,41,43,61,73,85,91,93,113. Expand
Cyclotomic integers and finite geometry
The most powerful method for the study of finite geometries with regular or quasiregular automorphism groups G is to translate their definition into an equation over the integral group ring 2[G] andExpand
An experimental search and new combinatorial designs via a generalisation of cyclotomy
Cyclotomy can be used to construct a variety of combinatorial designs, for example, supplementary difference sets, weighing matrices and T -matrices. These designs may be obtained by using linearExpand
Group invariant weighing matrices
  • M. Tan
  • Mathematics, Computer Science
  • Des. Codes Cryptogr.
  • 2018
TLDR
This work extends the usual concept of multipliers to group rings with cyclotomic integers as coefficients and combines it with the field descent method and rational idempotents to develop new non-existence results. Expand
Bijections Between Group Rings Preserving Character Sums
TLDR
This work exhibits some, in general nonhomomorphic, bijections between finite groups which preserve the absolute value of character sums. Expand
A survey on the skew energy of oriented graphs
The skew energy of an oriented graph was introduced by Adiga, Balakrishnan and So in 2010, as one of various generalizations of the energy of an undirected graph. Let G be a simple undirected graph,Expand
Some Infinite Series of Weighing Matrices From Hadamard Matrices

References

SHOWING 1-10 OF 89 REFERENCES
An infinite family of skew-weighing matrices
We verify the skew weighing matrix conjecture for orders 2t·7, t≥3 a positive integer, by showing that orthogonal designs (1,k) exist for all k=0,1,…,2t·7−1 in order 2t·7.
The skew - weighing matrix conjecture
We review the history of the skew-weighing matrix conjecture and show that there exist skew-symmetric weighing matrices W (21.2t, k) for all k=0,l,.....,21.2t I, t ≥ 4 a positive integer. Hence thereExpand
Semi Williamson type matrices and the W(2n, n) conjecture
Four (1, -1, OJ-matrices of order m, X = (Xi;), y = (Yi;), Z = (Z;}), U = (Ui;) satisfying (i) XX T + yyT + ZZT + UU T = 2mlm ,
On inequivalent weighing matrices
A weighing matrix W = W(n,k) of order n and weight k is a square matrix of order n, with entries 0, +1 aud -1 which satisfies WWT = kIn. Tools such as Smith Normal Form, profile, maximum integer andExpand
New Hadamard matrices and conference matrices obtained via Mathon's construction
TLDR
A formulation, via (1, −1) matrices, of Mathon's construction for conference matrices is given and a new family ofconference matrices of order 5⋅92t+1 + 1,t ≥ 0 is derived. Expand
On the excess of Hadamard matrices
TLDR
Improved upper bounds are given for σ ( n ) and a procedure is described to find all row-sum or column-sum vectors of an Hadamard matrix with given excess. Expand
On Composition of Four-Symbol δ-Codes and Hadamard Matrices
It is shown that key instruments for composition of four-symbol 6-codes are the Lagrange identity for polynomials, a certain type of quasisymmetric sequences (i.e., a set of normal or near normalExpand
Orthogonal (0,1,-1) matrices
We study the conjecture: There exists a square (0,l,-l)-matrix W = W(w,k) of order w satisfying WWT= kIw for all k = 0, 1,..., w when w = 0 (mod 4). We prove the conjecture is true for 4, 8, 12, 16,Expand
Constructing Hadamard matrices from orthogonal designs
TLDR
The Hadamard conjecture is that hadamard matrices exist for all orders 1,2, 4t where t ~ 1 is an integer and the results obtained strongly support the conjecture. Expand
Construction of Williamson type matrices
Recent advances in the construction of Hadamard matrices have depeaded on the existence of Baumert-Hall arrays and four (1, −1) matrices A B C Dof order m which are of Williamson type, that is theyExpand
...
1
2
3
4
5
...