Document Type
Journal Article
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 = Xj Xi and (iv) X1XT1 + X2XT2 + X3XT3 + X4X T4 = 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 ¼(s2+3) to construct new orthogonal designs, including new OD(2s2+6; 1, 1, 2, 2, s2, s2).
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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.