Orthogonal Arrays with Circulant Property: Construction, Analysis and Applications to fMRI Experiments

Abstract

Orthogonal arrays have been widely used in many experiments, but they do not exist for any size. Recently, orthogonal arrays with circulant property receive great attention and are applied in many fields such as stream cypher cryptanalysis and functional magnetic resonance imaging. Since circulant Hadamard matrices, that can be viewed as orthogonal arrays of symbols two and strength two, have been conjectured nonexistence, circulant almost orthogonal arrays (CAOA) are considered. In this talk, we propose a systematic construction to this new class of designs. Complete difference sets (CDS) are also introduced and applied for the construction of CAOA. We not only prove the equivalence relation of CDS and CAOA, but also construct CAOA of any prime power symbols. We further apply these designs to fMRI experiments, demonstrating that our constructed designs have better properties than the traditional designs in terms of cost-efficiency. This is a joint work with my postdoctoral research fellow Dr. Yuan-Lung Lin of Institute of Statistical Science, Academia Sinica, and Professor Jason Ming-Hung Kao of Arizona State University.