Corpus ID: 17599078

Group developed weighing matrices

  title={Group developed weighing matrices},
  author={K. Arasu and J. Hollon},
  journal={Australas. J Comb.},
A weighing matrix is a square matrix whose entries are 1, 0 or −1, such 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 will answer the question of existence for 318 such matrices of order and weight both below 100. At the end, we are left with 98 open cases out of a possible 1,022… Expand
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
Cohomology-Developed Matrices -- constructing families of weighing matrices and automorphism actions
The aim of this work is to construct families of weighing matrices via their automorphism group action. This action is determined from the $0,1,2$-cohomology groups of the underlying abstract group.Expand
Group invariant weighing matrices
  • M. Tan
  • Mathematics, Computer Science
  • Des. Codes Cryptogr.
  • 2018
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
Investigation of Communication and Radar System Optimization: New Computational and Theoretical Methods
A new asymptotically orthogonal type of matrix is defined with computational examples given along with infinite theoretical families and the optimality of binary sequences is discussed with searches for sequences with minimal sumof-square autocorrelation giving rise to an order 39 matrix with large determinant. Expand
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
New Nonexistence Results on Circulant Weighing Matrices
A circulant weighing matrix $W = (w_{i,j}) \in CW(n,k)$ is a square matrix of order $n$ and entries $w_{i,j}$ in $\{-1, 0, +1\}$ such that $WW^T=kI_n$. In his thesis, Strassler gave tables of knownExpand


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
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
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
Study of proper circulant weighing matrices with weight 9
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
On circulant and two-circulant weighing matrices
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
Hadamard matrices of order 764 exist
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
Circulant weighing matrices
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
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
Wieferich pairs and Barker sequences
We show that if a Barker sequence of length n > 13 exists, then either n = 189 260 468 001 034 441 522 766 781 604, or n > 2 · 1030. This improves the lower bound on the length of a long BarkerExpand
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.