On good matrices, skew Hadamard matrices and optimal designs

In two-level factorial experiments and in other linear models the coefficients of the unknown parameters can take one out of two values. When the number of observations is a multiple of four, the D-optimal design is a Hadamard matrix. Skew Hadamard matrices are of special interest due to their use, among others, in constructing D-optimal weighing designs for n=3(mod4). A method is given for constructing skew Hadamard matrices which is based on the construction of good matrices. The construction is achieved through an algorithm which is also presented and relies on the discrete Fourier transform. It is known that good matrices of order n, exist for all odd n=<35 and n=127. In this paper, we give for the first time all non-equivalent circulant good matrices of odd order 33=