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  • Conference proceedings
  • © 2015

Algebraic Design Theory and Hadamard Matrices

ADTHM, Lethbridge, Alberta, Canada, July 2014

  • 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

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 133)

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Table of contents (21 papers)

  1. Front Matter

    Pages i-xi
  2. On Good Matrices and Skew Hadamard Matrices

    • Gene Awyzio, Jennifer Seberry
    Pages 13-28
  3. Divisible Design Digraphs

    • Dean Crnković, Hadi Kharaghani
    Pages 43-60
  4. New Symmetric (61,16,4) Designs Obtained from Codes

    • Dean Crnković, Sanja Rukavina, Vladimir D. Tonchev
    Pages 61-69
  5. D-Optimal Matrices of Orders 118, 138, 150, 154 and 174

    • Dragomir Ž.-Doković, Ilias S. Kotsireas
    Pages 71-82
  6. Periodic Golay Pairs of Length 72

    • Dragomir Ž.-Doković, Ilias S. Kotsireas
    Pages 83-92
  7. Classifying Cocyclic Butson Hadamard Matrices

    • Ronan Egan, Dane Flannery, Padraig Ó Catháin
    Pages 93-106
  8. On Symmetric Designs and Binary 3-Frameproof Codes

    • Chuan Guo, Douglas R. Stinson, Tran van Trung
    Pages 125-136
  9. An Algorithm for Constructing Hjelmslev Planes

    • Joanne L. Hall, Asha Rao
    Pages 137-147
  10. Mutually Unbiased Biangular Vectors and Association Schemes

    • W. H. Holzmann, H. Kharaghani, S. Suda
    Pages 149-157
  11. A Simple Construction of Complex Equiangular Lines

    • Jonathan Jedwab, Amy Wiebe
    Pages 159-169
  12. Inner Product Vectors for Skew-Hadamard Matrices

    • Ilias S. Kotsireas, Jennifer Seberry, Yustina S. Suharini
    Pages 171-187
  13. Twin Bent Functions and Clifford Algebras

    • Paul C. Leopardi
    Pages 189-199
  14. A Note on Order and Eigenvalue Multiplicity of Strongly Regular Graphs

    • A. Mohammadian, B. Tayfeh-Rezaie
    Pages 209-212
  15. Trades in Complex Hadamard Matrices

    • Padraig Ó Catháin, Ian M. Wanless
    Pages 213-221
  16. The Hunt for Weighing Matrices of Small Orders

    • Ferenc Szöllősi
    Pages 223-234

About this book

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.

Keywords

  • Hadamard matrices
  • algebraic design theory
  • coding theory
  • combinatorics
  • computer security
  • quantum information theory
  • matrix theory
  • information and communication, circuits

Editors and Affiliations

  • School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, USA

    Charles J. Colbourn

Bibliographic Information

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access