I will quickly remind what self dual binary error correcting codes are and why they are useful. Then I will explain their relation to arithmetic, here unimodular lattices. Some years ago Volker Puppe has observed that odd- dimensional manifolds with involutions with finite fixed set yield self dual binary codes. In a joint paper we prove that all self dual codes come from involutions on 3-manifolds, which in some sense are rigid. I have extended this to all odd-dimensional manifolds of dimension > 1. This relation suggests a new (?) construction for self dual codes, which we call the box product. This gives a surprisingly simple way to get important lattices like E_8 or E_16 from very simple manifolds.