Presented by: 
Padraig Keane, UQ
Date: 
Tue 13 Nov, 3:00 pm - 4:00 pm
Venue: 
Room 442, Building 67
Hadamard matrices are (1,-1)-matrices which meet Hadamard's maximal determinant bound. Such matrices have a rigid combinatorial structure which gives rise to symmetric block designs. Hadamard matrices and block designs have many applications in signals processing, coding theory, the design of experiments, quantum computing, etc.
 
There are natural definitions of automorphisms for both types of structure. In both cases regular group actions give rise to algebraic structures of independent interest. I will discuss how these algebraic structures fit together, and provide a complete classification of Hadamard matrices supporting both structures. This classification 
can be used to address a number of problems in the literature.
 
The talk is suitable for a general audience, and presupposes only a knowledge of linear algebra and elementary group theory.