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Full-Text Articles in Physical Sciences and Mathematics
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
Faculty of Informatics - Papers (Archive)
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.
Orthogonal Designs Of Kharaghani Type: I, C. Koukouvinos, Jennifer Seberry
Orthogonal Designs Of Kharaghani Type: I, C. Koukouvinos, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We use an array given in H. Kharaghani, Arrays for orthogonal designs, J. Combin. Designs, 8 (2000), 166-173, to obtain infinite families of 8-variable Kharaghani type orthogonal designs, OD(8t; hi, kl, kl, kl, k2, k2, k2, k2), where k1 and k2 must be the sum of two squares. In particular we obtain infinite families of 8-variable Kharaghani type orthogonal designs, OD(8t; k, k, k, k, k, k, k, k). For odd t orthogonal designs of order ≡ 8( mod 16) can have at most eight variables.
Some Results On Kharaghani Type Orthogonal Designs, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Some Results On Kharaghani Type Orthogonal Designs, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
In this paper we give a general theorem which can be used to multiply the length of amicable sequences keeping the amicability property and the type of the sequences. As a consequence we have that if there exist two, four or eight amicable sequences of length m and type (al, a2), (al, a2, a3, a4) or (al, a2, …, as) then there exist amicable sequences of length ℓ ≡ 0 (mod m) and of the same type. We also present a theorem that produces a set of 2v amicable sequences from a set of v (not necessary amicable) sequences and …