Generalized Hadamard Matrices and Applications
Org:
Aidan Roy and Ada Chan (University of Waterloo and York University)
[
PDF]
 ROBERT CRAIGEN, University of Manitoba
Some Circulant Generalized Weighing matrices [PDF]

An elementary construction produces new classes of circulant generalized weighing matrices of socalled "Butson type" (i.e., whose entries are complex roots of unity) with parameters GW$(nN,n^2)$ for all positive integers $n, N$ such that $n \leq N$. We also discuss some generalizations and context. This was work done with Warwick de Launey before his recent death.
 HADI KHARAGHANI, University of Lethbridge
Mutually unbiased complex weighing matrices [PDF]

A $k$complex weighing matrix of order $n$ and weight $p$ is a matrix $CW(n,p)$ of order $n$ with entries consisting of the $k$th root of unity and $WW^*=pI_n$. Two $k$complex $CW(n,p)$, $H,K$ are called {\it unbiased} if the absolute value of the entries of $HK^*$ equal $\sqrt{p}$. The class of mutually unbiased $k$complex $CW(n,p)$s for small values of $n$ and $p$ will be discussed. This is a joint work with D. Best and H. Ramp.
 AIDAN ROY, University of Waterloo
Generalized Hadamard matrices and quantum measurements [PDF]

The columns of a unitary matrix $M$ may be thought of as a von Neumann measurement in quantum mechanics. When the entries of $M$ are highly structured, such as in a generalized Hadamard matrix, the measurement may prove particularly useful in quantum computing. I will give three instances of this phenomenon and describe the combinatorics involved in each: mutually unbiased bases, weighted complex $2$designs, and the entanglementassisted capacity of a graph.
 ALYSSA SANKEY, University of New Brunswick
TypeII matrices associated with 2graphs and weighted strongly regular graphs [PDF]

The class of typeII matrices includes Hadamard matrices and spin models. The Nomura algebra of a typeII matrix is the BoseMesner algebra of an association scheme.
Since spin models are contained in their Nomura algebras, we consider typeII matrices associated with known schemes. Indeed, they exist in connection with strongly regular graphs, certain distanceregular graphs, and other combinatorial objects.
In this talk we investigate typeII matrices, 2graphs and weighted strongly regular graphs.
Handling of online submissions has been provided by the CMS.