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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Necessary and Sufficient Conditions for two Variable Orthogonal Designs in Order 44: Addendum

S. Georgiou*! and 1, C. Koukouvinos2, M. Mitrouli1, Jennifer Seberry3
1Department of Mathematics, University of Athens, Panepistemiopolis 15784, Athens, Greece.
2Department of Mathematics, National Technical University of Athens, Zografou 15773, Athens, Greece.
3School of IT and Computer Science, University of Wollongong, Wollongong, NSW, 2522, Australia.
  • Published: 31/08/2000

Abstract

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 four circulant matrices.

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Citation
S. Georgiou*! and , C. Koukouvinos, M. Mitrouli, Jennifer Seberry. Necessary and Sufficient Conditions for two Variable Orthogonal Designs in Order 44: Addendum[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 034. 60-64. DOI: .