Hadamard Matrices: Constructions using Number Theory and Linear Algebra

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.

Emeritus Professor Mieko Yamada of Kanazawa University graduated from Tokyo Woman's Christian University and received her PhD from Kyusyu University in 1987. She has taught at Tokyo Woman's Christian University, Konan University, Kyushu University, and Kanazawa University. Her areas of research are combinatorics, especially Hadamard matrices, difference sets and codes. Her research approach for combinatorics is based on number theory and algebra. She is a foundation fellow of Institute of Combinatorics and its Applications (ICA). She is an author of 51 papers in combinatorics and number theory.

Emeritus Professor Jennifer Seberry graduated from University of New South Wales and received her PhD in Computation Mathematics from La Trobe University in 1971. She has held positions at the Australian National University, The University of Sydney, University College, The Australian Defence Force Academy (ADFA), The University of New South Wales, and University of Wollongong. She served as a head of Department of Computer Science of ADFA and a director of Centre for Computer Security Research of ADFA at University of Wollongong. She has published over 450 papers and eight books in Hadamard matrices, orthogonal designs, statistical designs, cryptology, and computer security.