Space-time codes based on quaternion algebras of small volume

We have seen in [13] a new reduction method for the decoding of 2×2 algebraic space-time codes, called algebraic reduction as been introduced. Algebraic codes such that the volume of the Dirichlet’s polyhedron of its units group is small are better suited for decoding using the method of algebraic reduction. In this paper, we propose a new framework for constructing a space-time code whose algebraic reduction behaves better than the one of the Golden code.