HADAMARD MATRICES

Jacket matrices constructed from Hadamard matrices and generalized Hadamard matrices

Power Hadamard matrices

We introduce power Hadamard matrices, in order to study the structure of (group) generalized Hadamard matrices, Butson (generalized) Hadamard matrices and other related orthogonal matrices, with which they share certain common characteristics. The new objects turn out to be as interesting, and perhaps as useful, as the objects that motivated them. We develop a basic theory of power Hadamard mat...

Hadamard and Conference Matrices

We discuss new constructions of Hadamard and conference matrices using relative difference sets. We present the first example of a relative (n, 2, n − 1, n−2 2 )-difference set where n − 1 is not a prime power.

Circulant Hadamard Matrices

Note. The determinant of a circulant matrix is an example of a group determinant, where the group is the cyclic group of order n. In 1880 Dedekind suggested generalizing the case of circulants (and more generally group de­ terminants for abelian groups) to arbitrary groups. It was this suggestion that led Frobenius to the creation group of representation theory. See [1] and the references therein.

Parametrizing complex Hadamard matrices

Abstract. The purpose of this paper is to introduce new parametric families of complex Hadamard matrices in two different ways. First, we prove that every real Hadamard matrix of order N ≥ 4 admits an affine orbit. This settles a recent open problem of Tadej and Życzkowski [11], who asked whether a real Hadamard matrix can be isolated among complex ones. In particular, we apply our construction...