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Full-Text Articles in Physical Sciences and Mathematics
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.
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 …
Necessary And Sufficient Conditions For Some Two Variable Orthogonal Designs In Order 44, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Necessary And Sufficient Conditions For Some Two Variable Orthogonal Designs In Order 44, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We give a new algorithm which allows us to construct new sets of sequences with entries from the commuting variables 0, ± a, ± b, ± c, ± d with zero autocorrelation function. We show that for twelve cases if the designs exist they cannot be constracted using four circulant matrices in the Goethals-Seidel array. Further we show that the necessary conditions for the existence of an OD(44; s1, s2) are sufficient except possibly for the following 7 cases: (7, 32) (8, 31), (9, 30) (9, 33) (11,30) (13, 29) (15, 26) which could not be found because of the …