A new method for constructing T-matrices

Authors

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

RIS ID

13265

Publication Details

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.