Distance properties of expander codes
  We study the minimum distance of codes defined on bipartite graphs. Weight spectrum and the minimum distance of a random ensemble of such codes are computed. It is shown that if the vertex codes have minimum distance $\ge 3$, the overall code is asymptotically good, and sometimes meets the Gilbert-Varshamov bound.   Constructive families of expander codes are presented whose minimum distance asymptotically exceeds the product bound for all code rates between 0 and 1. 
Alexander Barg and Gilles Zemor