Algebraic Theory of Orthogonal Designs

Abstract

As we saw in the last chapter, it is possible to obtain some non-trivial necessary conditions for the existence of orthogonal designs just by considering the equations that the coefficient matrices of an orthogonal design must satisfy. The ad-hoc procedures we give in the last chapter can, with difficulty, be pursued further. However, these procedures quickly become inadequate. To properly describe the solution to the “algebraic problem of orthogonal designs”, it is necessary to discuss the theory of quadratic and bilinear forms. Only then can the “algebraic problem” be put in proper perspective.