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.

scholarly journals Construction of generalized rotations and quasi-orthogonal matrices

2019 ◽  
Vol 7 (1) ◽  
pp. 107-113
Author(s):  
Luis Verde-Star
Keyword(s):  
Image Processing ◽  
Hadamard Matrices ◽  
Complex Numbers ◽  
Data Communications ◽  
Matrix Representations ◽  
Orthogonal Matrices ◽  
Orthogonal Designs ◽  
The Matrix ◽  
The One

Abstract We propose some methods for the construction of large quasi-orthogonal matrices and generalized rotations that may be used in applications in data communications and image processing. We use certain combinations of constructions by blocks similar to the one used by Sylvester to build Hadamard matrices. The orthogonal designs related with the matrix representations of the complex numbers, the quaternions, and the octonions are used in our construction procedures.

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 Amicable orthogonal designs

1976 ◽  
Vol 14 (2) ◽  
pp. 303-314 ◽  
Author(s):  
Peter J. Robinson
Keyword(s):  
Hadamard Matrices ◽  
Orthogonal Designs ◽  
Image Position

A powerful tool in the construction of orthogonal designs has been amicable orthogonal designs. Recent results in the construction of Hadamard matrices has led to the need to find amicable orthogonal designs A, B in order n and of types (u1, U2, …, u6) and (ν1, ν2, …, νr) respectively satisfying At = -A, Bt = B, and ABt = BAt withFor simplicity, we say A, B are amicable orthogonal designs of type (u1, u2, …, us; v1, v2, …, vr).We completely answer the question in order 8 by showing (1, 2, 2, 2; 8), (1, 2, 4; 2, 2, 4), (2, 2, 3; 2, 6), (7, 1, 7) and those designs derived from the above are the only possible.We use our results to obtain new orthogonal designs in order 32.

scholarly journals Hadamard Matrices, Orthogonal Designs and Construction Algorithms

Designs 2002 ◽  
2003 ◽  
pp. 133-205 ◽  
Author(s):  
Stelios Georgiou ◽  
Christos Koukouvinos ◽  
Jennifer Seberry
Keyword(s):  
Hadamard Matrices ◽  
Orthogonal Designs ◽  
Construction Algorithms
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