Complex weighing matrices and orthogonal designs

Galois fields G,F(q2) are used to obtain a new infinite family of complex weighing matrices. CW(q+l,q), q =1 (mod 8), and type P = [R – S S* - R*] where R and S are symmetric complex circulants. These matrices are used to construct orthogonal designs. Some unsolved cases of Geramita and Geramita are also settled.