Hadamard matrices, orthogonal designs and construction algorithms

Authors:
Stelios Georgiou;Christos Koukouvinos;Jennifer Seberry
Affiliations:
Department of Mathematics, National Technical University of Athens, Zografou 15773, Athens, Greece;Department of Mathematics, National Technical University of Athens, Zografou 15773, Athens, Greece;School of IT and Computer Science, University of Wollongong, Wollongong, NSW 2522, Australia
Venue:
DESIGNS 2002
Year:
2003

Citing 18
Cited 5

Number theory in science and communication

Number theory in science and communication
Hadamard matrices of order 28 with automorphism groups of order two

Journal of Combinatorial Theory Series A
Hadamard matrices of the Williamson type of order 4·Cm, m=p·Cq an exhaustive search for m=33

Discrete Mathematics
Numerical recipes in Pascal: the art of scientific computing

Numerical recipes in Pascal: the art of scientific computing
A new restriction on the lengths of Golay complementary sequences

Journal of Combinatorial Theory Series A
Williamson matrices of orders 4.29 and 4.31

Journal of Combinatorial Theory Series A
Williamson matrices of order 4n for n=33,35,39

Discrete Mathematics
The non-equivalent circulant D-optimal designs for n ≡ 2 mod 4, n≤54, n=66

Journal of Combinatorial Theory Series A
Classification of Hadamard matrices of order 28 with Hall sets

Discrete Mathematics
Classification of Hadamard matrices of order 28

Discrete Mathematics
Using MPI: portable parallel programming with the message-passing interface

Using MPI: portable parallel programming with the message-passing interface
PVM: Parallel virtual machine: a users' guide and tutorial for networked parallel computing

PVM: Parallel virtual machine: a users' guide and tutorial for networked parallel computing
On the orthogonal designs of order 24

Discrete Applied Mathematics - Coding, cryptography and computer security
Bounds on the number of affine, symmetric, and Hadamard designs and matrices

Journal of Combinatorial Theory Series A
On sequences with zero autocorrelation and orthogonal designs

Journal of Combinatorial Theory Series A
UNIX Network Programming: Networking APIs: Sockets and XTI

UNIX Network Programming: Networking APIs: Sockets and XTI
The existence of a Bush-type Hadamard matrix of order 36 and two new infinite classes of symmetric designs

Journal of Combinatorial Theory Series A
Classification of Hadamard matrices of order 44 with automorphisms of order 7

Discrete Mathematics

Hadamard ideals and Hadamard matrices with two circulant cores

European Journal of Combinatorics
2-(31,15,7), 2-(35,17,8) and 2-(36,15,6) designs with automorphisms of odd prime order, and their related Hadamard matrices and codes

Designs, Codes and Cryptography
Non-redundant precoding and PAPR reduction in MIMO OFDM systems with ICA based blind equalization

IEEE Transactions on Wireless Communications
Review: Independent component analysis for multiple-input multiple-output wireless communication systems

Signal Processing
A sign test for detecting the equivalence of Sylvester Hadamard matrices

Numerical Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

We discuss algorithms for the construction of Hadamard matrices. We include discussion of construction using Williamson matrices, Legendre pairs and the discret Fourier transform and the two circulants construction.Next we move to algorithms to determine the equivalence of Hadamard matrices using the profile and projections of Hadamard matrices. A summary is then given which considers inequivalence of Hadamard matrices of orders up to 44.The final two sections give algorithms for constructing orthogonal designs, short amicable and amicable sets for use in the Kharaghani array.