For every prime power q = 3 (mod 8) we prove the existence of (q; x, 0, y, y)-partitions of GF(q) with q = x2 + 2y2 for some x, y, which are very useful for constructing SDS, T-matrices and Hadamard matrices. We discuss the transformations of (q; x, 0, y, y)-partitions and, by using the partitions, construct generalized cyclotomic classes which have properties similar to those of classical cyclotomic classes. Thus we provide a new construction for T-matrices of order q2.