For every prime power q ≡ 7 mod 16, we obtain the (q; a, b, c, d)–partitions of G F (q), with odd integers a, b, c, d, a ≡ ± 1 mod 8 such that q = a2 + 2(b2 + c2 + d2) and d2 = b2 + 2ac + 2bd. Hence for each value of q the construction of SDS becomes equivalent to building a (q; a, b, c, d)–partition. The latter is much easier than the former. We give a new construction for an infinite family of regular Hadamard matrices of order 4q2 by 16th power cyclotomic classes.