Hadamard Matrices and Their Applications

K. J. Horadam

Published by Princeton University Press 2007

Hadamard Matrices and Their Applications

K. J. Horadam

https://doi.org/10.1515/9781400842902

Overview
Contents

About this book

In Hadamard Matrices and Their Applications, K. J. Horadam provides the first unified account of cocyclic Hadamard matrices and their applications in signal and data processing. This original work is based on the development of an algebraic link between Hadamard matrices and the cohomology of finite groups that was discovered fifteen years ago. The book translates physical applications into terms a pure mathematician will appreciate, and theoretical structures into ones an applied mathematician, computer scientist, or communications engineer can adapt and use.

The first half of the book explains the state of our knowledge of Hadamard matrices and two important generalizations: matrices with group entries and multidimensional Hadamard arrays. It focuses on their applications in engineering and computer science, as signal transforms, spreading sequences, error-correcting codes, and cryptographic primitives.

The book's second half presents the new results in cocyclic Hadamard matrices and their applications. Full expression of this theory has been realized only recently, in the Five-fold Constellation. This identifies cocyclic generalized Hadamard matrices with particular "stars" in four other areas of mathematics and engineering: group cohomology, incidence structures, combinatorics, and signal correlation.

Pointing the way to possible new developments in a field ripe for further research, this book formulates and discusses ninety open questions.

Author / Editor information

K. J. Horadam is Professor of Mathematics and leads the Information Theory and Security Research Group at RMIT University, Melbourne, Australia.

Reviews

"The material on applications of Hadamard matrices is, in a word, excellent. Researchers and students in communications, cryptography, and experimental design will find this to be an excellent source, while research mathematicians will find the second part just as interesting. The book is insightful and rewarding. It is definitely a book that I will have on my most accessible shelf."—Charles Colbourn, Arizona State University

"This book will surely be a welcome contribution to the existing literature. The book can be used by researchers in the early stages of their work and as a source for a course in the subject."—Christos Koukouvinos, National Technical University of Athens

This book is a marvelous and timely contribution to a rapidly developing field, with new oflshoots into physics, engineering and algebra. . . . Overall, the text gives an excellent introduction to Hadamard matrices, a masterful short survey of applications the field of communications, and a wild ride through these new algebraic tools and new combinatorial objects of study being spawned by this modern approach. Absolutely up-to-date and useful, his is a must-have text for all researchers in this field, and a must-read for aspiring researchers of Hadamard matrices, their generalizations, and their applications.---Robert Craigen, Mathematical Reviews

Topics

Frontmatter Publicly Available Download PDF	i
Contents Publicly Available Download PDF	vii
Preface. ACKNOWLEDGEMENTS Requires Authentication Unlicensed Licensed Download PDF	xi
Chapter One. Introduction Requires Authentication Unlicensed Licensed Download PDF	1
PART 1. Hadamard Matrices, Their Applications and Generalisations
Chapter Two. Hadamard Matrices Requires Authentication Unlicensed Licensed Download PDF	9
Chapter Three. Applications in Signal Processing, Coding and Cryptography Requires Authentication Unlicensed Licensed Download PDF	27
Chapter Four. Generalised Hadamard Matrices Requires Authentication Unlicensed Licensed Download PDF	62
Chapter Five. Higher Dimensional Hadamard Matrices Requires Authentication Unlicensed Licensed Download PDF	92
PART 2. Cocyclic Hadamard Matrices
Chapter Six. Cocycles and Cocyclic Hadamard Matrices Requires Authentication Unlicensed Licensed Download PDF	113
Chapter Seven. The Five-fold Constellation Requires Authentication Unlicensed Licensed Download PDF	139
Chapter Eight. Bundles and Shift Action Requires Authentication Unlicensed Licensed Download PDF	162
Chapter Nine. The Future: Novel Constructions and Applications Requires Authentication Unlicensed Licensed Download PDF	192
Bibliography Requires Authentication Unlicensed Licensed Download PDF	238
Index Requires Authentication Unlicensed Licensed Download PDF	259

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