Strong amicable orthogonal designs and amicable Hadamard matrices

Amicable orthogonal designs have renewed interest because of their use in mobile communications. We show the existence of strong amicable orthogonal designs, AOD(n: 1, n - 1; 1, n - 1), for n = pr + 1, p ≡ 3 (mod 4) a prime and for n = 2r, n a non-negative integer in a form more suitable for communications. Unfortunately the existence of amicable Hadamard matrices is not enough to demonstrate the existence of strong amicable orthogonal designs.