Some Infinite Series of 2-Weighing and 3-Weighing Matrices from Hadamard Matrices

2018 ◽  
Vol 9 (12) ◽  
pp. 2165-2168
Author(s):  
Gopal Prajapati ◽  
Mithilesh Kumar Singh
Keyword(s):  
Infinite Series ◽  
Hadamard Matrices ◽  
Weighing Matrices

Some Infinite Series of Weighing Matrices From Hadamard Matrices

2018 ◽  
Vol 54 (3) ◽  
pp. 217-221
Author(s):  
Gopal Prajapati ◽  
◽  
Mithilesh Kumar Singh
Keyword(s):  
Infinite Series ◽  
Hadamard Matrices ◽  
Weighing Matrices

scholarly journals Short Amicable sets and Kharaghani type orthogonal designs

2001 ◽  
Vol 64 (3) ◽  
pp. 495-504 ◽  
Author(s):  
Christos Koukouvinos ◽  
Jennifer Seberry
Keyword(s):  
Hadamard Matrices ◽  
Weighing Matrices ◽  
Orthogonal Designs

Dedicated to Professor George SzekeresShort amicable sets were introduced recently and have many applications. The construction of short amicable sets has lead to the construction of many orthogonal designs, weighing matrices and Hadamard matrices. In this paper we give some constructions for short amicable sets as well as some multiplication theorems. We also present a table of the short amicable sets known to exist and we construct some infinite families of short amicable sets and orthogonal designs.

TWO-CIRCULANT HADAMARD MATRICES, WEIGHING MATRICES, AND RYSER'S CONJECTURE

2018 ◽  
Vol 3 (94) ◽  
pp. 2-9 ◽  
Author(s):  
Yu. N. Balonin ◽  
◽  
A. M. Sergeev ◽  
Keyword(s):  
Hadamard Matrices ◽  
Weighing Matrices

scholarly journals Symmetric Hadamard matrices of order 116 and 172 exist

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Olivia Di Matteo ◽  
Dragomir Ž. Ðoković ◽  
Ilias S. Kotsireas
Keyword(s):  
Infinite Series ◽  
Hadamard Matrices ◽  
Matching Problem

AbstractWe construct new symmetric Hadamard matrices of orders 92, 116, and 172. While the existence of those of order 92 was known since 1978, the orders 116 and 172 are new. Our construction is based on a recent new combinatorial array (GP array) discovered by N. A. Balonin and J. Seberry. For order 116 we used an adaptation of an algorithm for parallel collision search. The adaptation pertains to the modification of some aspects of the algorithm to make it suitable to solve a 3-way matching problem. We also point out that a new infinite series of symmetric Hadamard matrices arises by plugging into the GP array the matrices constructed by Xia, Xia, Seberry, and Wu in 2005.

scholarly journals New symmetric designs from regular Hadamard matrices

10.37236/1339 ◽  
1997 ◽  
Vol 5 (1) ◽  
Author(s):  
Yury J. Ionin
Keyword(s):  
Positive Integer ◽  
Prime Power ◽  
Hadamard Matrices ◽  
Weighing Matrices ◽  
Symmetric Designs ◽  
Parameter Values

For every positive integer $m$, we construct a symmetric $(v,k,\lambda )$-design with parameters $v={{h((2h-1)^{2m}-1)}\over{h-1}}$, $k=h(2h-1)^{2m-1}$, and $\lambda =h(h-1)(2h-1)^{2m-2}$, where $h=\pm 3\cdot 2^d$ and $|2h-1|$ is a prime power. For $m\geq 2$ and $d\geq 1$, these parameter values were previously undecided. The tools used in the construction are balanced generalized weighing matrices and regular Hadamard matrices of order $9\cdot 4^d$.

Circles on lattices and Hadamard matrices

2019 ◽  
pp. 2-9 ◽  
Author(s):  
N. A. Balonin ◽  
M. B. Sergeev ◽  
J. Seberry ◽  
O. I. Sinitsyna
Keyword(s):  
Hadamard Matrices ◽  
Lattice Points ◽  
Practical Significance ◽  
Upper And Lower Bounds ◽  
Problem Size ◽  
Orthogonal Matrices ◽  
Video Information ◽  
Scientific Schools ◽  
Gauss Theorem ◽  
Triangular Numbers

Introduction: The Hadamard conjecture about the existence of Hadamard matrices in all orders multiple of 4, and the Gauss problem about the number of points in a circle are among the most important turning points in the development of mathematics. They both stimulated the development of scientific schools around the world with an immense amount of works. There are substantiations that these scientific problems are deeply connected. The number of Gaussian points (Z3 lattice points) on a spheroid, cone, paraboloid or parabola, along with their location, determines the number and types of Hadamard matrices.Purpose: Specification of the upper and lower bounds for the number of Gaussian points (with odd coordinates) on a spheroid depending on the problem size, in order to specify the Gauss theorem (about the solvability of quadratic problems in triangular numbers by projections onto the Liouville plane) with estimates for the case of Hadamard matrices. Methods: The authors, in addition to their previous ideas about proving the Hadamard conjecture on the base of a one-to-one correspondence between orthogonal matrices and Gaussian points, propose one more way, using the properties of generalized circles on Z3 .Results: It is proved that for a spheroid, the lower bound of all Gaussian points with odd coordinates is equal to the equator radius R, the upper limit of the points located above the equator is equal to the length of this equator L=2πR, and the total number of points is limited to 2L. Due to the spheroid symmetry in the sector with positive coordinates (octant), this gives the values of R/8 and L/4. Thus, the number of Gaussian points with odd coordinates does not exceed the border perimeter and is no less than the relative share of the sector in the total volume of the figure.Practical significance: Hadamard matrices associated with lattice points have a direct practical significance for noise-resistant coding, compression and masking of video information.

A new application of quasi monotone sequences and quasi power increasing sequences to factored infinite series

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5105-5109
Author(s):  
Hüseyin Bor
Keyword(s):  
Infinite Series ◽  
Summability Factors ◽  
Monotone Sequences ◽  
Power Increasing Sequences ◽  
Weaker Conditions ◽  
Increasing Sequences

In this paper, we generalize a known theorem under more weaker conditions dealing with the generalized absolute Ces?ro summability factors of infinite series by using quasi monotone sequences and quasi power increasing sequences. This theorem also includes some new results.

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