CHARACTERIZATION OF INFORMATION MATRICES FOR BALANCED 2-LEVEL FRACTIONAL FACTORIAL-DESIGNS OF ODD RESOLUTION DERIVED FROM 2-SYMBOL SIMPLE ARRAYS

We consider a balanced fractional 2m factorial design of resolution 2l+1 which permits estimation of all factorial effects up through l-factor interactions under the situation in which all (l+1)-factor and higher order interactions are to be negligible for an integer l satisfying [m/2]<l less-than-or-equal-to m, where [x] denotes the greatest integer not exceeding x. This paper investigates algebraic structure of the information matrix of such a design derived from a simple array through that of an atomic array. We obtain an explicit expression for the irreducible matrix representation based on the above design and its algebraic properties. The results in this paper will be useful to characterize the designs under consideration.