Construction of E8 as a left ideal of the Silver algebra

Silver code was originally discovered in [1-4] for 2×2 multiple-input multiple-output (MIMO) channels. This code can be constructed algebraically from a particular cyclic division algebra, Silver algebra. Space-Time Block Codes (STBC) based on an order of a cyclic division algebra of index 2 such that the volume of the Dirichlet’s polyhedron of the group of units is small, are better suited for decoding using the method of algebraic reduction since the approximation error is smaller [16]. In this paper we propose a new construction of E8-lattice from Silver algebra and whose algebraic reduction behaves better than the one of the Golden code.