Algebra seminar tomorrow

[Hollanti Camilla]

Welcome! 

Camilla

Szöllösi Ferenc, Institute of Mathematics, Budapest University of Technology and Economics

New results on generalized Hadamard matrices

* Wednesday 17 October 2012,   15:15,   room U510

A square $\\pm1$ matrix $H$ of order $n$ is a real Hadamard matrix if $HH^T=nI$, i.e.\\ $H$ has pairwise orthogonal rows. Deciding the existence of real Hadamard matrices is a long standing open problem in design theory. It is easy to see that if $n>2$ and a real Hadamard matrix exists then $n=4k$ for some positive integer $k$. The famous Hadamard conjecture proposes that Hadamard matrices do exists for every $k$. There are various generalizations of Hadamard matrices. For example, one can consider complex Hadamard matrices where the entries are some $q$th roots of unity. Such matrices are called Butson-type Hadamard matrices and are denoted by $\\mathrm{BH}(n,q)$. In this talk we review some of the very recent advances in this field, and discuss the existence and structural properties of $\\mathrm{BH}(n,q)$ matrices for $q=2,4,6$ and for a general prime number $q$.