Hadamard Matrices And Their Applications

Author : K. J. Horadam
Publisher : Princeton University Press
Page : 280 pages
File Size : 43,5 Mb
Release : 2012-01-06
Category : Mathematics
ISBN : 9781400842902

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Hadamard Matrices and Their Applications by K. J. Horadam Pdf

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 explains the state of our knowledge of Hadamard matrices and two important generalizations: matrices with group entries and multidimensional Hadamard arrays. It focuses on their applications in engineering and computer science, as signal transforms, spreading sequences, error-correcting codes, and cryptographic primitives. The book's second half presents the new results in cocyclic Hadamard matrices and their applications. Full expression of this theory has been realized only recently, in the Five-fold Constellation. This identifies cocyclic generalized Hadamard matrices with particular "stars" in four other areas of mathematics and engineering: group cohomology, incidence structures, combinatorics, and signal correlation. Pointing the way to possible new developments in a field ripe for further research, this book formulates and discusses ninety open questions.

Author : S. S. Agaian
Publisher : Unknown
Page : 238 pages
File Size : 41,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662192713

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Hadamard Matrices and Their Applications by S. S. Agaian Pdf

Author : Jennifer Seberry,Mieko Yamada
Publisher : John Wiley & Sons
Page : 352 pages
File Size : 44,8 Mb
Release : 2020-08-25
Category : Mathematics
ISBN : 9781119520245

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Hadamard Matrices by Jennifer Seberry,Mieko Yamada Pdf

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.

Author : S.S. Agaian
Publisher : Springer
Page : 231 pages
File Size : 42,6 Mb
Release : 2006-12-07
Category : Mathematics
ISBN : 9783540397403

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Hadamard Matrices and Their Applications by S.S. Agaian Pdf

Author : Rao K. Yarlagadda,John E. Hershey
Publisher : Springer Science & Business Media
Page : 120 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461563136

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Hadamard Matrix Analysis and Synthesis by Rao K. Yarlagadda,John E. Hershey Pdf

Hadamard Matrix Analysis and Synthesis: With Applications to Communications and Signal/Image Processing presents the basic concepts of Sylvester's construction of Hadamard matrices, the eigenvalue-eigenvector decompositions, along with its relationship to Fourier transforms. Relevant computational structures are included for those interested in implementing the Hadamard transform. The 2-dimensional Hadamard transform is discussed in terms of a 1- dimensional transform. The applications presented touch on statistics, error correction coding theory, communications signaling, Boolean function analysis and synthesis, image processing, sequence theory (maximal length binary sequences, composite sequences, and Thue-Morse sequences) and signal representation. An interesting application of the Hadamard transform to images is the Naturalness Preserving Transform (NPT), which is presented. The NPT provides a way to encode an image that can be reconstructed when it is transmitted through a noisy or an unfriendly channel. The potential applications of the Hadamard transform are wide and the book samples many of the important concepts among a vast field of applications of the transform. Hadamard Matrix Analysis and Synthesis: With Applications to Communications and Signal/Image Processing serves as an excellent reference source and may be used as a text for advanced courses on the topic.

Author : Yi Xian Yang
Publisher : Unknown
Page : 340 pages
File Size : 50,8 Mb
Release : 2001
Category : Mathematics
ISBN : UOM:39015054187284

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Theory and Applications of Higher-dimensional Hadamard Matrices by Yi Xian Yang Pdf

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.

Author : Yang Yi Xian
Publisher : Springer
Page : 320 pages
File Size : 50,7 Mb
Release : 2002-02-28
Category : Mathematics
ISBN : 0792370619

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Theory and Applications of Higher-Dimensional Hadamard Matrices by Yang Yi Xian Pdf

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.

Author : S. S. Agaian
Publisher : SPIE-International Society for Optical Engineering
Page : 0 pages
File Size : 55,6 Mb
Release : 2011
Category : Hadamard matrices
ISBN : 0819486477

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Hadamard Transforms by S. S. Agaian Pdf

The Hadamard matrix and Hadamard transform are fundamental problem-solving tools in a wide spectrum of scientific disciplines and technologies, such as communication systems, signal and image processing (signal representation, coding, filtering, recognition, and watermarking), digital logic (Boolean function analysis and synthesis), and fault-tolerant system design. Hadamard Transforms intends to bring together different topics concerning current developments in Hadamard matrices, transforms, and their applications. Each chapter begins with the basics of the theory, progresses to more advanced topics, and then discusses cutting-edge implementation techniques. The book covers a wide range of problems related to these matrices/transforms, formulates open questions, and points the way to potential advancements. Hadamard Transforms is suitable for a wide variety of audiences, including graduate students in electrical and computer engineering, mathematics, or computer science. Readers are not presumed to have a sophisticated mathematical background, but some mathematical background is helpful. This book will prepare readers for further exploration and will support aspiring researchers in the field.

Author : Charles J. Colbourn
Publisher : Springer
Page : 259 pages
File Size : 49,6 Mb
Release : 2015-09-03
Category : Mathematics
ISBN : 9783319177298

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Algebraic Design Theory and Hadamard Matrices by Charles J. Colbourn Pdf

This volume develops the depth and breadth of the mathematics underlying the construction and analysis of Hadamard matrices, and their use in the construction of combinatorial designs. At the same time, it pursues current research in their numerous applications in security and cryptography, quantum information, and communications. Bridges among diverse mathematical threads and extensive applications make this an invaluable source for understanding both the current state of the art and future directions.​ ​The existence of Hadamard matrices remains one of the most challenging open questions in combinatorics. Substantial progress on their existence has resulted from advances in algebraic design theory using deep connections with linear algebra, abstract algebra, finite geometry, number theory, and combinatorics. Hadamard matrices arise in a very diverse set of applications. Starting with applications in experimental design theory and the theory of error-correcting codes, they have found unexpected and important applications in cryptography, quantum information theory, communications, and networking.

Author : Themistocles M. Rassias,Vijay Gupta
Publisher : Springer
Page : 741 pages
File Size : 48,6 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9783319312811

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Mathematical Analysis, Approximation Theory and Their Applications by Themistocles M. Rassias,Vijay Gupta Pdf

Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

Author : Yi Xian Yang,Xin Xin Niu,Cheng Qing Xu
Publisher : Chapman and Hall/CRC
Page : 0 pages
File Size : 55,7 Mb
Release : 2010-03-24
Category : Computers
ISBN : 143981807X

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Theory and Applications of Higher-Dimensional Hadamard Matrices, Second Edition by Yi Xian Yang,Xin Xin Niu,Cheng Qing Xu Pdf

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.

Author : Tor Helleseth,Dilip Sarwate,Hong-Yeop Song,Kyeongcheol Yang
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 44,6 Mb
Release : 2005-06
Category : Computers
ISBN : 9783540260844

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Sequences and Their Applications - SETA 2004 by Tor Helleseth,Dilip Sarwate,Hong-Yeop Song,Kyeongcheol Yang Pdf

This book constitutes the thoroughly refereed post-proceedings of the Third International Conference on Sequences and Their Applications, SETA 2004, held in Seoul, Korea in October 2004. The 30 revised full papers presented together with 4 invited survey articles were carefully selected during two rounds of reviewing and improvement from initially 59 submissions. The papers are organized in topical sections on complexity of sequences, perfect sequences, sequence construction, sequences modulo z, sequence generator properties and applications, multi-dimensional sequences, optics and OFDM applications, and polynomials and functions.

Author : Yi Xian Yang,Cheng Qing Xu
Publisher : CRC Press
Page : 440 pages
File Size : 55,9 Mb
Release : 2019-08-30
Category : Electronic
ISBN : 036738440X

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Theory and Applications of Higher-dimensional Hadamard Matrices by Yi Xian Yang,Cheng Qing Xu Pdf

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.

Author : Claude Carlet,Alexander Pott
Publisher : Springer
Page : 465 pages
File Size : 42,5 Mb
Release : 2010-09-07
Category : Computers
ISBN : 9783642158742

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Sequences and Their Applications - SETA 2010 by Claude Carlet,Alexander Pott Pdf

This book constitutes the proceedings of the 6th International Conference on Sequences and Their Applications held in Paris, France, in September 2010.

Author : Charles R. Johnson
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 46,6 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821801543

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Matrix Theory and Applications by Charles R. Johnson Pdf

This volume contains the lecture notes prepared for the AMS Short Course on Matrix Theory and Applications, held in Phoenix in January, 1989. Matrix theory continues to enjoy a renaissance that has accelerated in the past decade, in part because of stimulation from a variety of applications and considerable interplay with other parts of mathematics. In addition, the great increase in the number and vitality of specialists in the field has dispelled the popular misconception that the subject has been fully researched.