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Necessary And Sufficient Conditions For Three And Four Variable Orthogonal Designs In Order 36, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We use a new algorithm to find new sets of sequences with entries from {0, ±a, ±b, ±c, ±d}, on the commuting variables a, b, c, d, with zero autocorrelation function. Then we use these sequences to construct a series of new three and four variable orthogonal designs in order 36. We show that the necessary conditions plus (.s1, s2, s3, s4) not equal to 12816 18 816 221313 26721 36 816 4889 12825 191313 23 424 289 9 381015 8899 14425 22 916 are sufficient for the existence of an OD(36; s1, s2 s3, s4) constructed using four circulant …