Algebraic Design Theory and Hadamard Matrices
ADTHM, Lethbridge, Alberta, Canada, July 2014
Editors: Colbourn, Charles J. (Ed.)
Free Preview- Explores the applications of Hadamard matrices in experimental design, digital communication, cryptography, and quantum physics
- Examines the current state of the field and avenues of future research
- Develops connections between abstrct algebra, linear algebra, finite geometry, and number theory
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- About this book
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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.
- Table of contents (21 chapters)
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On (−1, 1)-Matrices of Skew Type with the Maximal Determinant and Tournaments
Pages 1-11
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On Good Matrices and Skew Hadamard Matrices
Pages 13-28
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Suitable Permutations, Binary Covering Arrays, and Paley Matrices
Pages 29-42
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Divisible Design Digraphs
Pages 43-60
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New Symmetric (61,16,4) Designs Obtained from Codes
Pages 61-69
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Table of contents (21 chapters)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Algebraic Design Theory and Hadamard Matrices
- Book Subtitle
- ADTHM, Lethbridge, Alberta, Canada, July 2014
- Editors
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- Charles J. Colbourn
- Series Title
- Springer Proceedings in Mathematics & Statistics
- Series Volume
- 133
- Copyright
- 2015
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-17729-8
- DOI
- 10.1007/978-3-319-17729-8
- Hardcover ISBN
- 978-3-319-17728-1
- Softcover ISBN
- 978-3-319-37218-1
- Series ISSN
- 2194-1009
- Edition Number
- 1
- Number of Pages
- XI, 259
- Number of Illustrations
- 26 b/w illustrations, 69 illustrations in colour
- Topics
