A well-known algebraic approach for constructing generalized Hadamard matrices is the recent theory of cocyclic development. This theory establishes a central link between cohomology of finite groups and combinatorics. Research on cocyclic generalised Hadamard matrices focuses on finding families of groups whose second cohomology group can be used to construct generalised Hadamard matrices.
In this project we will survey the current theory of cocyclic generalised Hadamard matrices; study the so-called 5-fold constellation and its connection to generalised Hadamard matrices and other combinatorial objects, such as relative difference sets, divisible designs, and sequences with good autocorrelation; and search for open questions and low hanging results.
Peter is studying a Bachelor of Science Advanced Research at Monash University, double majoring in mathematics and computer science. His main interests within mathematics are of algebra and discrete mathematics, though he will happily indulge other areas as well. A favourite pastime of Peter’s is playing the piano.