Constructions of Orthonormal Lattices and Quaternion Division Algebras for Totally Real Number Fields

摘要

We describe some constructions of orthonormal lattices in totally real subfields of cyclotomic fields, obtained by endowing their ring of integers with a trace form. We also describe constructions of quaternion division algebras over such fields. Orthonormal lattices and quaternion division algebras over totally real fields find use in wireless networks in ultra wideband communication, and we describe the application.