Hadamard Matrices

Constructions using Number Theory and Linear Algebra

Jennifer Seberry, Mieko Yamada

• Publisher: Wiley
• Year: 2020
• Print ISBN: 9781119520245
• eBook ISBN: 9781119520276
• Edition: 1
• Topic: Mathématiques
• Subtopic: Théorie des nombres

Up-to-date resource on Hadamard matrices

Hadamard Matrices: Constructions using Number Theory and Algebra provides students with a discussion of the basic definitions used for Hadamard Matrices as well as more advanced topics in the subject, including:

• Gauss sums, Jacobi sums and relative Gauss sums
• Cyclotomic numbers
• Plug-in matrices, arrays, sequences and M-structure
• Galois rings and Menon Hadamard differences sets
• Paley difference sets and Paley type partial difference sets
• Symmetric Hadamard matrices, skew Hadamard matrices and amicable Hadamard matrices
• A discussion of asymptotic existence of Hadamard matrices
• Maximal determinant matrices, embeddability of Hadamard matrices and growth problem for Hadamard matrices

The book can be used as a textbook for graduate courses in combinatorics, or as a reference for researchers studying Hadamard matrices.

Utilized in the fields of signal processing and design experiments, Hadamard matrices have been used for 150 years, and remain practical today. Hadamard Matrices combines a thorough discussion of the basic concepts underlying the subject matter with more advanced applications that will be of interest to experts in the area.

Table of contents

• Cover
• Title Page
• Copyright Page
• Contents
• List of Tables
• List of Figures
• Preface
• Acknowledgments
• Acronyms
• Introduction
• Chapter 1 Basic Definitions
• Chapter 2 Gauss Sums, Jacobi Sums, and Relative Gauss Sums
• Chapter 3 Plug-In Matrices
• Chapter 4 Arrays: Matrices to Plug-Into
• Chapter 5 Sequences
• Chapter 6 M-structures
• Chapter 7 Menon Hadamard Difference Sets and Regular Hadamard Matrices
• Chapter 8 Paley Hadamard Difference Sets and Paley Type Partial Difference Sets
• Chapter 9 Skew Hadamard, Amicable, and Symmetric Matrices
• Chapter 10 Skew Hadamard Difference Sets
• Chapter 11 Asymptotic Existence of Hadamard Matrices
• Chapter 12 More on Maximal Determinant Matrices
• Appendix A Hadamard Matrices
• Appendix B List of sds from Cyclotomy
• Appendix C Further Research Questions
• References
• Index
• EULA