A New Formula for the Minimum Distance of an Expander Code

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 a $(m,n,d,\gamma,1-\varepsilon)$ expander bipartite graph.