We introduce the class of weak amicable T-matrices and use it to construct a class of orthogonal designs, OD(4(1+p)q;q,q,q,q,pq,pq,pqpq)for p = 1 and for p a prime power 3 (mod 4), and all odd q, q 21. This class includes new Plotkin arrays of order 24, 40, 56 and for the first time, of orders 8q, q {9,11,13,15,17,19,21}.
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