A new method for constructing T-matrices

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

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This article was origianlly published as Xia, M, Xia, T, Seberry, J and Zuo, G, A new method for constructing T-matrices , Australasian Journal of Combinatorics, 32, 2005, 61-78.

Abstract

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