  Orbits of graphs under the operation edge local complementation (ELC) are
defined. We show that the ELC orbit of a bipartite graph corresponds to the
equivalence class of a binary linear code. The information sets and the minimum
distance of a code can be derived from the corresponding ELC orbit. By
extending earlier results on local complementation (LC) orbits, we classify the
ELC orbits of all graphs on up to 12 vertices. We also give a new method for
classifying binary linear codes, with running time comparable to the best known
algorithm.
