Prof. Ilias S. Kotsireas, Wilfrid Laurier University

Legendre Pairs are combinatorial objects with a rich 20+ years history. Their main application is that they furnish a structured form of the Hadamard conjecture and they have been studied by several authors. We bring into bear a number of Linear Algebraic concepts and tools, in the context of Legendre Pairs. This allows us to improve existing computational schemes to search efficiently for Legendre Pairs. Preliminary implementations indicate that using custom-tailored FFT-type algorithms for computing the DFT of odd-length input vectors clearly out-performs previous techniques used for this purpose.
Joint work with Dr. Shirani M. Perera, ERAU, Florida, United States.