New Constructing of regular Hadamard matrices

Authors

Tianbing Xia, University of WollongongFollow
Jennifer Seberry, University of WollongongFollow
M. Xia, Central China Normal University, ChinaFollow

RIS ID

21814

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.

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.