Orthogonal Designs of Kharaghani Type: II

Orthogonal Designs of Kharaghani Type: I

We use an array given in H. Kharaghani, Arrays for orthogonal designs, J. Combin. Designs, 8 (2000), 166-173, to obtain infinite families of 8-variable Kharaghani type orthogonal designs, OD(8t; hi, kl, kl, kl, k2, k2, k2, k2), where k1 and k2 must be the sum of two squares. In particular we obtain infinite families of 8-variable Kharaghani type orthogonal designs, OD(8t; k, k, k, k, k, k, k, k...

All triples for orthogonal designs of order 40

The use of amicable sets of eight circulant matrices and four negacyclic matrices to generate orthogonal designs is relatively new. We find all 1841 possible orthogonal designs of order 40 in three variables, using only these new techniques.

The asymptotic existence of orthogonal designs

Given any -tuple ( s1, s2, . . . , s ) of positive integers, there is an integer N = N ( s1, s2, . . . , s ) such that an orthogonal design of order 2 ( s1 + s2 + · · ·+ s ) and type ( 2s1, 2 s2, . . . , 2 s ) exists, for each n ≥ N . This complements a result of Eades et al. which in turn implies that if the positive integers s1, s2, . . . , s are all highly divisible by 2, then there is a ful...

Linked system of symmetric group divisible designs of type II

The linked systems of symmetric group divisible designs of type II is introduced, and several examples are obtained from affine resolvable designs and mutually UFS Latin squares. Furthermore, an equivalence between such symmetric group divisible designs and some association schemes with 5-classes is provided.

Orthogonal designs and MDS self-dual codes