Circulant Orthogonal Array: Its Construction and Application to fMRI Experiments

• Activity Number: 255
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Frederick Phoa*
• Companies: Academia Sinica
• Keywords: Orthogonal Array ; General Difference Set ; Functional Magnetic Resonance Imaging ; Circulant Matrix ; Factorial Designs

Abstract

Orthogonal arrays have been widely used in various experiments, but they do not exist for any size. Recently, circulant-type orthogonal arrays are proposed and needed in many fields such as stream cypher cryptanalysis. 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 are considered such as fMRI experiments. In this talk, we propose a series of new designs called circulant almost orthogonal arrays (COA). Complete difference sets (CDS) are also introduced and applied for the construction of COA. We not only prove the equivalence relation of CDS and COA, but also construct circulant almost orthogonal arrays of any prime power symbols. We further apply this class of new designs to planning the functional magnetic resonance imaging (fMRI) experiments.