Abstract: Stolz and Teichner have conjectured that the moduli space of D=1+1, N=(0,1) QFTs provides a geometric model for Topological Modular Forms. Some important building blocks in this moduli space are the holomorphic superconformal field theories, and the conjecture leads to predictions about the possible values the supersymmetric index of such SCFTs can take. Specifically, the conjecture leads one to predict the existence of SCFTs of small nonzero index, and that the minimal possible index depends in an interesting way on the central charge of the SCFT. I will explain a construction of some SCFTs of indexes equal to the predicted minimal values. The construction leads to a new divisibility result in the seemingly unrelated field of algebraic coding theory. Based on joint work with Davide Gaiotto and Noam D Elkies.