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Full-Text Articles in Physical Sciences and Mathematics
Necessary And Sufficient Conditions For Two Variable Orthogonal Designs In Order 44: Addendum, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Necessary And Sufficient Conditions For Two Variable Orthogonal Designs In Order 44: Addendum, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
In our recent paper Necessary and sufficient conditions for some two variable orthogonal designs in order 44, Koukouvinos, Mitrouli and Seberry leave 7 cases unresolved. Using a new algorithm given in our paper A new algorithm for computer searches for orthogonal designs by the present four authors we are able to finally resolve all these cases. This note records that the necessary conditions for the existence of two variable designs constructed using four circulant matrices are sufficient. In particular of 484 potential cases 404 cases have been found, 68 cases do not exist and 12 cases cannot be constructed using …
New Orthogonal Designs And Sequences With Two And Three Variables In Order 28, C. Koukouvinos, Jennifer Seberry
New Orthogonal Designs And Sequences With Two And Three Variables In Order 28, C. Koukouvinos, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We give new sets of sequences with entries from {0, ±a, ±b, ±c} on the commuting variables a, b, c and zero autocorrelation function. Then we use these sequences to construct some new orthogonal de-signs. We show the necessary conditions for the existence of an OD(28; s1, s2, s3) plus the condition that (s1, s2, s3) ≠ (1,5,20) are sufficient conditions for the existence of an OD(28; s1, s2, s3). We also show the necessary conditions for the existence of an OD(28; s1, s2, s3) constructed using four circulant matrices are sufficient conditions for the existence of 4 — NPAF(s1, …