Lattices from maximal orders into quaternion algebras

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Processo FAPESP: 2011/12657-9

We propose an algebraic framework to construct dense lattices from maximal orders of a quaternion algebra whose center is an imaginary quadratic field. This work extends [21] where a method called algebraic reduction has been proposed to efficiently decode the Golden code [14]. In particular, we propose four new constructions of E-8 lattice from left ideals of maximal orders of some quaternion algebras with centers Q(root-d), d = 1,2,3,7. (C) 2014 Elsevier B.V. All rights reserved.