Theory and Applications of Higher-Dimensional Hadamard Matrices
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内容提要：
This is the first book on higher-dimensional Hadamard matrices and their applications in telecommunications and information security. It is divided into three parts according to the dimensions of the Hadamard matrices treated. The first part stresses the classical 2-dimensional Walsh and Hadamard matrices. Fast algorithms, updated constructions, exitence results, and their generalised forms are presented. The second part deals with the lower-dimensional cases, e.g. 3-, 4-, and 6-dimensional Walsh and Hadamard matrices and transforms. The third part is the key part, which investigates the N-dimensional Hadamard matrices of order 2, which have been proved equivalent to the well known H-Boolean functions and the perfect binary arrays of order 2. After introducing the definitions of the regular, proper, improper, and generalized higher-dimensional Hadamard matrices, many theorems about the existence and constructions are presented. Perfec binary arrays, generalized perfect arrays, and the orthogonal designs are also used to construct new higher-dimensional Hadamard matrices. The many open problems in the study of the theory of higher-dimensional Hadamard matrices which are also listed in the book will encourage further research. .
This volume will appeal to researchers and graduate students whose work involves signal processing, coding, information security and applied discrete mathematics. ... 目录：
Preface. Part I Two-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 前言：
Just over one hundred years ago, in 1893, Jacques Hadamard found 'binary' (±1) matrices of orders 12 and 20 whose rows (resp. columns) were pairwise orthogonal. These matrices satisfy the determinantal upper bound for 'binary' matrices. Hadamard actually proposed the question of seeking the maximal determinant of matrices with entries on the unit circle, but his name has become associated with the question concerning real (binary) matrices. Hadamard was not the first person to study these matrices. For example, J. J. Sylvester had found, in ..
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