Amicable Hadamard matrices and amicable orthogonal designs

Authors

Jennifer Seberry, University of WollongongFollow
Mieko Yamada

Publication Details

Jennifer Seberry and Mieko Yamada, Amicable Hadamard matrices and amicable orthogonal designs, Utilitas Mathematica, 40, (1991), 179-192.

Abstract

New constructions for amicable orthogonal designs are given. These new designs then give new amicable Hadamard matrices and new skew-Hadamard matrices. In particular we show that if p is the order of normalized amicable Hadamard matrices there are normalized amicable Hadamard matrices of order (p - 1)^u + 1, u > 0 an odd integer.

Tables are given for the existence of amicable and skew-Hadamard matrices of orders 2^tq, t ≥ 2 an integer, q(odd)≤2000. This gives further evidence to support the conjecture that "for every odd integer q there exists an integer t (dependent on q) so that there is a skew-Hadamard matrix of order 2^tq."