In this talk I will show that all binary, self-dual codes can be constructed using the Hilbert-symbol pairing of S-integers of global fields. This is inspired by M. Kreck and V. Puppe´s result that all such codes can be realized by an involution on a three-manifold, along with the folklore analogy that Spec(Z) ´behaves like´ a three manifold in cohomological aspects. If time permits, I will also talk about the questions concerning generalization to higher dimensions and topological implications.