We will apply the theory of arithmetic groups and their associated automorphic forms to construct highly symmetric error correcting codes. It has been previously conjectured that such symmetric codes do not exist. The codes are built using edge-transitive Ramanujan graphs which were constructed by Lubotzky-Samuels-Vishne (as special cases of Ramanujan complexes). The lecture is aimed toward a general audience and all notions from either CS of Math will be defined and explained. (Based on joint work with Tali Kaufman).