New Constructing of regular Hadamard matrices

T. Xia, University of Wollongong
J. Seberry, University of Wollongong
M. Xia, Central China Normal University, China

Article comments

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.

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 = 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.