#### RIS ID

21814

#### Abstract

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* = *a*^{2} + 2(*b*^{2} + *c*^{2} + *d*^{2}) and *d*^{2} = *b*^{2} + 2*ac* + 2*bd*. 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 4*q*^{2} by 16th power cyclotomic classes.

## Publication Details

This article was originally published as Xia, T, Seberry, J and Xia, M, New Constructing of regular Hadamard matrices, WSEAS Transactions on Mathematics, 5(2006), 1068-1073.