Weak amicable T‐matrices and Plotkin arrays

We introduce the class of weak amicable T‐matrices and use it to construct a class of orthogonal designs, 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}. © 2006 Wiley Periodicals, Inc. J Combin Designs 16: 44–52, 2008