On the orthogonal designs of order 24

On amicable orthogonal designs of order 8

Some new amicable orthogonal designs of order 8 are found as part of a complete search of the equivalence classes for orthogonal designs OD(8; 1, 1, 1, 1), OD(8; 1, 1, 1, 4), OD(8; 1, 1, 2, 2), OD(8; 1, 1, 1, 2), OD (8; 1, 1, 2, 4), OD(8; 1, 1, 1, 3), OD(8; 1, 1, 2, 3), OD(8; 1, 1, 1, 5) and OD(8; 1, 1, 3, 3). 2000 Mathematics subject classification (Amer. Math. Soc.): 05B30, 15A36.

On Full Orthogonal Designs in Order 56

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. Keywords : Construction, sequences, circulant matrices, amicable sets, orthogonal designs, AMS Subject Classification: Primary 05B15, 05B20, Secondary 62K05. Publication D...

On the Amicability of Orthogonal Designs

Although it is known that the maximum number of variables in two amicable orthogonal designs of order 2n p, where p is an odd integer, never exceeds 2n+2, not much is known about the existence of amicable orthogonal designs lacking zero entries that have 2n+2 variables in total. In this paper we develop two methods to construct amicable orthogonal designs of order 2n p where p odd, with no zero...

Three variable full orthogonal designs of order 56

Using the doubling lemma, amicable sets of eight circulant matrices and four complementary negacyclic matrices, we show that all full triples are types of orthogonal designs of order 56. This implies that all full orthogonal designs OD(2t7;x, y, 2t7− x− y) exist for any t ≥ 3.

Orthogonal designs of order 32 and 64 via computational algebra