Self-dual Codes over the Kleinian Four Group

Gerald Hoehn

Published 2000-05-26Version 1

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.