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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
Faculty of Informatics - Papers (Archive)
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.
Short Amicable Sets, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Short Amicable Sets, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Abstract: A pair of matrices X and Y are said to be amicable if XYT = YXT. In this paper, if X and Y are orthogonal designs, group generated or circulant on the group G, these will be denoted 2—SAS(n; ul, u2; G). Recently Kharaghani, in "Arrays for orthogonal designs", J. Combin. Designs, 8 (2000), 166-173, extended this concept to an amicable set, {Ai}2n, i=1, of 2n circulant matrices, which satisfy ∑(Aσ(2i-1)AT σ(2i-1) - Aσ(2i) AT (2i-1) = 0. In this paper we concentrate on constructing short amicable sets, which satisfy the same equation but contain four, called short, or …