Constructing Optimal Division Algebras for Space-Time Coding

In [1] the authors suggested that in order to derive energy efficient space-time MIMO codes from orders of the division algebras one should use maximal orders instead of natural ones. They also described the division algebras that have the best maximal orders in terms of minimum determinant vs. average power. However, they were able to construct division algebras that were optimal only in few separate cases. In this paper we are addressing this problem and giving an explicit construction for optimal division algebras of arbitrary degree in the case when the center is Q(i). We note that all the results of this paper can be found from [2]. The goal of this paper is to give a simple representation of construction methods of [2].