Lattices from maximal quaternion orders over totally real number fields

Abstract

In this paper we propose a framework to construct space-time codes over lattices in dimensions 4n via ideals from maximal orders of a quaternion algebra whose center is a totally real number field. For n = 1 and n = 2 it was possible to construct rotated versions of the densest lattices in their dimensions, D4 and E8. These constructions provide explicit forms for the generator matrix and other algebraic invariants allowing to analyze meaningful performance parameters for coding such as density, diversity and minimal product distance.