Three variable full orthogonal designs of order 56

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.

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 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.

New orthogonal designs and sequences with two and three variables in order 28

We give new sets of sequences with entries from f0; a;b; cg on the commuting variables a; b; c and zero autocorrelation function. Then we use these sequences to construct some new orthogonal designs .

Orthogonal designs of order 32 and 64 via computational algebra