Self-dual Codes over the Kleinian Four Group
  We introduce self-dual codes over the Kleinian four group K = Z_2 x Z_2 for a natural quadratic form on K^n and develop the theory.   Topics studied are: weight enumerators, mass formulas, classification up to length 8, neighbourhood graphs, extremal codes, shadows, generalized t-designs, lexicographic codes, the Hexacode and its odd and shorter cousin, automorphism groups, marked codes.   Kleinian codes form a new and natural fourth step in a series of analogies between binary codes, lattices and vertex operator algebras. This analogy will be emphasized and explained in detail. 
Gerald Hoehn