RIS ID
6436
Abstract
Call four type 1(1,-1) matrices, x1,x2,x3,x4; of the same group of order m (odd) with the properties (i) (Xi-I)T = -(Xi-I), i=1,2,3, (ii)XT4 = X4 and the diagonal elements are positive, (iii) XiXj = XjXi and (iv) X1XT1 + X2XT2+X3XT3 +X4XT4 = 4mIm, best matrices. We use a computer to give, for the first time, all inequivalent best matrices of odd order m ≤31. Inequivalent best matrices of order m, m odd, can be used to find inequivalent skew-Hadamard matrices of order 4m. We use best matrices of order 1/4(s2+3) to construct new orthogonal designs, including new OD(2s2+6;1,1,2,2,s2,s2).
Publication Details
This article was originally published as Georgiou, S, Koukouvinos, C and Seberry, J, On circulant best matrices and their applications, Linear and Multilinear Algebra, 48, 2001, 263-274. Copyright Taylor & Francis. Original journal available here.