The purpose of this seminar is to show how some error-correcting codes can be understood by means of appropriate commutative semigroups with given generators.  Given a group note that a fundamental way to provide a geometric structure is to specify a list of generators of the group that  gives rise to the word metric (The idea of studying a finitely generated group via the geometry of its metric goes back at least to the work of Dehn). This approach involves the description of several kinds of objects such as abelian groups, lattices, algebras and binomial ideals.