Algebraic Design Theory and Hadamard Matrices: ADTHM, Lethbridge, Alberta, Canada, July 2014

✍ Scribed by Charles J. Colbourn (eds.)

• Publisher: Springer International Publishing
• Year: 2015
• Tongue: English
• Leaves: 261
• Series: Springer Proceedings in Mathematics & Statistics 133
• Edition: 1
• Category: Library

✦ Synopsis

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

Front Matter....Pages i-xi
On (−1, 1)-Matrices of Skew Type with the Maximal Determinant and Tournaments....Pages 1-11
On Good Matrices and Skew Hadamard Matrices....Pages 13-28
Suitable Permutations, Binary Covering Arrays, and Paley Matrices....Pages 29-42
Divisible Design Digraphs....Pages 43-60
New Symmetric (61,16,4) Designs Obtained from Codes....Pages 61-69
D-Optimal Matrices of Orders 118, 138, 150, 154 and 174....Pages 71-82
Periodic Golay Pairs of Length 72....Pages 83-92
Classifying Cocyclic Butson Hadamard Matrices....Pages 93-106
Signed Group Orthogonal Designs and Their Applications....Pages 107-123
On Symmetric Designs and Binary 3-Frameproof Codes....Pages 125-136
An Algorithm for Constructing Hjelmslev Planes....Pages 137-147
Mutually Unbiased Biangular Vectors and Association Schemes....Pages 149-157
A Simple Construction of Complex Equiangular Lines....Pages 159-169
Inner Product Vectors for Skew-Hadamard Matrices....Pages 171-187
Twin Bent Functions and Clifford Algebras....Pages 189-199
A Walsh–Fourier Approach to the Circulant Hadamard Conjecture....Pages 201-208
A Note on Order and Eigenvalue Multiplicity of Strongly Regular Graphs....Pages 209-212
Trades in Complex Hadamard Matrices....Pages 213-221
The Hunt for Weighing Matrices of Small Orders....Pages 223-234
Menon–Hadamard Difference Sets Obtained from a Local Field by Natural Projections....Pages 235-249
BIRS Workshop 14w2199 July 11–13, 2014 Problem Solving Session....Pages 251-259

✦ Subjects

Combinatorics; Linear and Multilinear Algebras, Matrix Theory; Number Theory; Information and Communication, Circuits