Regular Hadamard Matrices, Maximum Excess and SBIBD

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

Article comments

This article was originally published as Xia, T, Xia, M and Seberry, J, Regular Hadamard Matrices, Maximum Excess and SBIBD, Australasian Journal of Combinatorics, 27, 2003, 263-275. Original journal available here.

Abstract

When k = q1, q2, q1q2, q1q4, q2q3N, q3q4N, q1, q2 and q3 are prime power, where q1 ≡ 1 (mod 4), q2 ≡ 3 (mod 8), q3 ≡ 5 (mod 8), q4 = 7 or 23, N = 2a3bt2, a, b = 0 or 1, t ≠ 0 is an arbitrary integer, we prove that there exist regular Hadamard matrices of order 4k2, and also there exist SBIBD(4k2, 2k2 + k, k2 + k). We find new SBIBD(4k2, 2k2 + k, k2 + k) for 233 values of k.