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.