A new formula for the minimum distance of an expander code

Abstract

An expander code is a binary linear code whose parity-check matrix is the bi-adjacency matrix of a bipartite expander graph. We provide a new formula for the minimum distance of such codes. We also provide a new proof of the result that $2(1-\varepsilon) \gamma n$ is a lower bound of the minimum distance of the expander code given by an $(m,n,d,\gamma,1-\varepsilon)$ expander bipartite graph.