Theory and Applications of Higher-Dimensional Hadamard Matrices

Drawing on the authors’ use of the Hadamard-related theory in several successful engineering projects, Theory and Applications of Higher-Dimensional Hadamard Matrices, Second Edition explores the applications and dimensions of Hadamard matrices. This edition contains a new section on the applications of higher-dimensional Hadamard matrices to the areas of telecommunications and information security.

The first part of the book presents fast algorithms, updated constructions, existence results, and generalized forms for Walsh and Hadamard matrices. The second section smoothly transitions from two-dimensional cases to three-, four-, and six-dimensional Walsh and Hadamard matrices and transforms. In the third part, the authors discuss how the n-dimensional Hadamard matrices of order 2 are applied to feed-forward networking, stream ciphers, bent functions, and error correcting codes. They also cover the Boolean approach of Hadamard matrices. The final part provides examples of applications of Hadamard-related ideas to the design and analysis of one-dimensional sequences and two-dimensional arrays.

The theory and ideas of Hadamard matrices can be used in many areas of communications and information security. Through the research problems found in this book, readers can further explore the fascinating issues and applications of the theory of higher-dimensional Hadamard matrices.

Yi Xian Yang is director and professor of the Information Security Center (ISC) at Beijing University of Posts and Telecommunications (BUPT). He is also director of the State Engineering Lab of Backup for Disaster Recovery. Dr. Yang received his Ph.D. in electrical engineering and communication systems from BU.
Xin Xin Niu and Cheng Qing Xu, Beijing University of Posts and Telecommunications

2-Dimensional CasesWalsh MatricesHadamard Matrices
Lower-Dimensional Cases3-Dimensional Hadamard MatricesMulti-Dimensional Walsh–Hadamard Transforms
General Higher-Dimensional Casesn-Dimensional Hadamard Matrices of Order 2General Higher-Dimensional Hadamard Matrices
Applications to Signal Design and AnalysisDesign and Analysis of SequencesDesign and Analysis of Arrays
Concluding Questions
Index