Optimal Expander Graphs from BIBD's, Their LDPC Codes and Decoding,   Tom Hoeholdt,   Technical University of Denmark,  Mon, 11 May, 2009,   11:30 a.m. A-143


In recent years there has been a lot of interest in codes based on graphs, in particular codes from bipartite graphs with good expansion properties. We present a construction of such codes and give results on their parameters and the decoding. We also show that graphs coming from balanced incomplete block designs, in particular from finite geometries, have very good expansion properties ( in some sense they are optimal ). Moreover we prove that a bipartite graph with a certain condition on the spectrum of the ardency matrix comes from a BIBD.