高維哈達瑪矩陳理論與應用（簡體書）

本書是國際上第一本有關高維哈達瑪矩陣及其在電信與信息安全領域中的應用專著《Theory and Applications of Higher Dimensional Hadamard Matrices》的修訂版，分為三個部分。第一部分重點研究經典的2維Walsh矩陣和哈達瑪矩陣，包括它們的快速算法、最新構造法、存在性結果及其一般性的推廣。第二部分考慮的是低維情形，例如，3-維、4-維和6-維Walsh和哈達瑪矩陣與變換。第三部分是全書的核心也是本書的獨特之處，研究了N-維2階哈達瑪矩陣，并證明了這類矩陣與著名的H-布爾函數和2階最佳二進陣列是等價的，由此，推導出了一系列有關高維2階哈達瑪矩陣的計數結果。本書中還羅列了許多有關高維哈達瑪矩陣理論研究和工程應用的公開問題。

Preface to the Second Edition
Preface to the First Edition
Part Ⅰ 2-Dimensional Cases
　Chapter 1 Walsh Matrices
1.1 Walsh Functions and Matrices
1.1.1 Definitions
1.1.2 Ordering
1.2 Orthogonality and Completeness
1.2.1 Orthogonality
1.2.2 Completeness
1.3 Walsh Transforms and Fast Algorithms
1.3.1 Walsh-Ordered Walsh-Hadamard Transforms
1.3.2 Hadamard-Ordered Walsh-Hadamard Transforms
Bibliography
Chapter 2 Hadamard Matrices
2.1 Definitions
2.1.1 Hadamard Matrices
2.1.2 Hadamard Designs
2.1.3 Williamson Matrices
2.2 Construction
2.2.1 General Constructions
2.2.2 Amicable Hadamard Matrices
2.2.3 Skew Hadamard Matrices
2.2.4 Symmetric Hadamard Matrices
2.3 Existence
2.3.1 Orth0gonal Designs and Hadamard Matrices
2.3.2 Existence Results
Bibliography
Part Ⅱ Lower-Dimensional Cases
　Chapter 3 3-Dimensional Hadamard Matrices
3.1 Definitions and Constructions
3.1.1 Definitions
3.1.2 Constructions Based on Direct Multiplications
3.1.3 Constructions Based on 2-Dimensional Hadamard Matrices
3.2 3-Dimensional Hadamard Matrices of Order 4k + 2
3.3 3-Dimensional Hadamard Matrices of Order 4k
3.3.1 Recursive Constructions of Perfect Binary Arrays
3.3.2 Quasi-Perfect Binary Arrays
3.3.3 3-Dimensional Hadamard Matrices Based on PBA(2m, 2m) and PBA(3.2m, 3.2m)
3.4 3-Dimensional Walsh Matrices
3.4.1 Generalized 2-Dimensional Walsh Matrices
3.4.2 3-Dimensional Walsh Matrices
3.4.3 3-Dimensional Pan-Walsh Matrices
3.4.4 Analytic Representations
Bibliography
　Chapter 4 Multi-Dimensional Walsh-Hadamard Transforms
4.1 Conventional 2-Dimensional Walsh-Hadamard Transforms
4.1.1 2-Dimensional Walsh-Hadamard Transforms
4.1.2 Definitions of 4-Dimensional Hadamard Matrices
4.2 Algebraic Theory of Higher-Dimensional Matrices
4.3 Multi-Dimensional Walsh-Hadamard Transforms
4.3.1 Transforms Based on 3-Dimensional Hadamard Matrices
4.3.2 Transforms Based on 4-Dimensional Hadamard Matrices
4.3.3 Transforms Based on 6-Dimensional Hadamard Matrices
Bibliography
Part Ⅲ General Higher-Dimensional Cases
　Chapter 5 n-Dimensional Hadamard Matrices of Order 2
5.1 Constructions of 2n Hadamard Matrices
5.1.1 Equivalence between 2n Hadamard Matrices and H-Boolean Functions
5.1.2 Existence of H-Boolean Functions
5.1.3 Constructions of H-Boolean Functions
5.2 Enumeration of 2 Hadamard Matrices
5.2.1 Classification of 24 Hadamard Matrices
5.2.2 Enumeration of 25 Hadamard Matrices
5.2.3 Enumeration of General 2n Hadamard Matrices
5.3 Applications
5.3.1 Strict Avalanche Criterion and H-Boolean Functions
5.3.2 Bent Functions and H-Boolean Functions
5.3.3 Reed-Muller Codes and H-Boolean Functions
Bibliography
　Chapter 6 General Higher-Dimensional Hadamard Matrices
6.1 Definitions, Existences and Constructions
6.1.1 n-Dimensional Hadamard Matrices of Order 2k
6.1.2 Proper and Improper n-Dimensional Hadamard Matrices
6.1.3 Generalized Higher-Dimensional Hadamard Matrices
6.2 Higher-Dimensional Hadamard Matrices Based on Perfect Binary Arrays
6.2.1 n-Dimensional Hadamard Matrices Based on PBAs
6.2.2 Construction and Existence of Higher-Dimensional PBAs
6.2.3 Generalized Perfect Arrays
6.3 Higher-Dimensional Hadamard Matrices Based on Orthogonal Designs
6.3.1 Definitions of Orthogonality
6.3.2 Higher-Dimensional Orthogonal Designs
6.3.3 Higher-Dimensional Hadamard Matrices from Orthogonal Designs
Bibliography
Part Ⅳ Applications to Signal Design and Analysis
　Chapter 7 Design and Analysis of Sequences
7.1 Sequences of Cryptographic Significance
7.1.1 Enumerating Boolean Functions of Cryptographic Significance
7.1.2 Constructing Boolean Functions of Cryptographic Significance
7.1.3 Correlation Immunity of Boolean Functions
7.1.4 Entropy Immunity of Feedforward Networks
7.2 Correlation Functions of Geometric Sequences
7.2.1 Onthe Correlation Functions of a Family of Gold-Geometric Sequences
7.2.2 On the Correlation Functions of a Family of Generalized Geometric Sequences
7.2.3 On the Correlation Functions of p-Ary d-Form Sequences
7.3 Sequence Pairs with Mismatched Filtering
7.3.1 Binary Sequences Pairs with Two-Level Autocorrelation Functions (BSPT)
7.3.2 Difference Set Pairs
7.3.3 Construction of BSPTs
7.3.4 Periodic Complementary Binary Sequence Pairs
7.4 Sequence Unusual Analysis
7.4.1 Boolean Neural Network Design
7.4.2 Linear Complexity and Random Sequences with Period 2n
7.4.3 Periodic Ambiguity Functions of EQC-Based TFHC
7.4.4 Auto-, Cross-, and Triple Correlations of Sequences
Bibliography
　Chapter 8 Design and Analysis of Arrays
8.1 Costas Arrays
8.1.1 Correlations of Costas Arrays
8.1.2 Algebraically Constructed Costas Arrays
8.1.3 Enumeration Limitation of Costas Arrays
8.2 Optical Orthogonal Codes
8.2.1 Parameters Bounds of Optical Orthogonal Codes
8.2.2 Truncated Costas Optical Orthogonal Codes
Bibliography
Concluding Questions
Index