Hadamard Matrices and Their Applications.

Print version record.

Cover; Title; Copyright; Contents; Preface; Chapter 1. Introduction; PART 1. HADAMARD MATRICES, THEIR APPLICATIONS AND GENERALISATIONS; Chapter 2. Hadamard Matrices; 2.1 Classical Constructions; 2.2 Equivalence Classes; 2.3 The First Link: Group Developed Constructions; 2.4 Towards the Hadamard Conjecture; Chapter 3 Applications in Signal Processing, Coding and Cryptography; 3.1 Spectroscopy: Walsh-Hadamard Transforms; 3.2 Error Correction: Hadamard Codes; 3.3 Signal Modulation and Separation: Hadamard Codes; 3.4 Signal Correlation: Perfect Sequences and Arrays.

3.5 Cryptography: Nonlinear FunctionsChapter 4 Generalised Hadamard Matrices; 4.1 Butson Matrices; 4.2 Complex Hadamard Matrices; 4.3 Generalised Hadamard Matrices; 4.4 Applications of Complex and Generalised Hadamard Matrices; 4.5 Unification: Generalised Butson Hadamard Matrices and Transforms; Chapter 5 Higher Dimensional Hadamard Matrices; 5.1 Classical Constructions; 5.2 Equivalence Classes; 5.3 Applications in Spectroscopy, Coding and Cryptography; 5.4 The Second Link: Cocyclic Construction; PART 2: COCYCLIC HADAMARD MATRICES; Chapter 6 Cocycles and Cocyclic Hadamard Matrices.

6.1 Cocycles and Group Cohomology6.2 Cocycles are Everywhere!; 6.3 Computation of Cocycles; 6.4 Cocyclic Hadamard Matrices; 6.5 The Cocyclic Hadamard Conjecture; Chapter 7 The Five-fold Constellation; 7.1 Factor Pairs and Extensions; 7.2 Orthogonality for Factor Pairs; 7.3 All the Cocyclic Generalised Hadamard Matrices; 7.4 The Five-fold Constellation; Chapter 8 Bundles and Shift Action; 8.1 Bundles and the Five-fold Constellation; 8.2 Bundles of Functions-- The Splitting Case; 8.3 Bundles of Cocycles-- The Central Case; 8.4 Shift Action -- The Central Case.

8.5 Shift Orbits -- The Central Splitting CaseChapter 9 The Future: Novel Constructions and Applications; 9.1 New Applications of Cocycles; 9.2 New Group Developed Generalised Hadamard Matrices; 9.3 New Cocyclic Generalised Hadamard Matrices; 9.4 New Hadamard Codes; 9.5 New Highly Nonlinear Functions; Bibliography; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; W; Y.

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 explain.

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