Short amicable sets and Kharaghani type orthogonal designs

Short amicable sets were introduced recently and have many applications. The construction of short amicable sets had lead to the construction of many orthogonal designs, weighing matrices and Hadamard matrices. In this paper we give some constructions for short amicable sets as well as some multiplication theorems. We also present a table of the short amicable sets known to exist and we construct some infinite families of short amicable sets and orthogonal designs.