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On Full Orthogonal Designs In Order 56, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Full Orthogonal Designs In Order 56, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
We find new full orthogonal designs in order 56 and show that of 1285 possible OD(56; s1, s2, s3, 56—s1—s2-s3) 163 are known, of 261 possible OD(56; s1, s2, 56—s1—s2) 179 are known. All possible OD(56; s1, 56 — s1) are known.
On Circulant Best Matrices And Their Applications, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Circulant Best Matrices And Their Applications, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
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).
On Full Orthogonal Designs In Order 72, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Full Orthogonal Designs In Order 72, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
We find new full orthogonal designs in order 72 and show that of 2700 possible OD(72; s1, s2, s3, 72—s1—s2—s3) 335 are known, of 432 possible OD(72; s1, s2, 72—si—s2) 308 are known. All possible OD(72; s1, 72 — s1) are known.