In joint work with Arne Winterhof (Austrian Academy of Sciences), we study properties of and constructions for Quaternary Legendre Pairs (qLPs), i.e. two -1,+1,i,-1-sequences of the same length with constant periodic autocorrelation sum -2. In contrast with binary Legendre pairs, it turns out that qLPs exist for even orders and that algebraic number theory, in particular, the theory of cyclotomic fields, provides an appropriate framework that allows us to elucidate certain of their properties that have been discovered experimentally. In addition, qLPs can be used to construct complex and real Hadamard matrices. Finally, some of the algebraic number theory obstructions in the context of qLPs, apply to binary Legendre Pairs, which leads to substantially improved algorithmic schemes for searching for these objects.

Bio: Ilias S. Kotsireas serves as a Computer Science Professor and the Director of the CARGO Lab at Wilfrid Laurier University, in Waterloo, Ontario, Canada. He serves on the Editorial Board of 11 international journals and as the Managing Editor of two Springer journals and the Editor in Chief of a Springer journal and a Birkhauser book series. He has organized a very large number of international conferences. His main research area is Design Theory. He served as Chair of the ACM SIGSAM and serves as a co-chair of the Applications of Computer Algebra Working Group. He has delivered more than 20 invited/plenary talks around the world.