Wojciech J. Gajda

Abstract:

With every linear code one can associate a lattice, and with every lattice - a theta function. It is then, perhaps, not surprising that there is a connection (a homomorphism!) between suitable spaces of codes and modular forms. What is remarkable, is the level of this resemblance: in both worlds there are functions invariant under an action of a group, notions of cusp forms and Hecke operators, also projections and lifts between different geni. The compatibility between these objects will be explained in the first part of the talk. This will prepare the ground for the second part: an adaptation of doubling method in the framework of binary linear codes. The new phenomena that will be presented are the effect of joint work with Thanasis Bouganis.