Lattice theoretic approach to space-time codes from division algebras

This master project on algebraic coding theory gathers various techniques from lattice theory, central simple algebras and algebraic number theory. The thesis begins with the formulation of the engineering problem into mathematical form. It presents how space-time codes appeared, and how we can construct codes based on Q(i)-central division algebras. More precisely, it is explained how we can build codes from cyclic division algebras; and a generalization is done with the introduction of crossed product algebras. The approach used is slightly more geometric than what is usually done in the literature. We also give slight generalization to known methods for analyzing minimum determinants of division algebra-based codes.