In 1996, Sipser and Spielman [12] constructed a family of linear-time decodable asymptotically good codes called expander codes. Recently, Barg and Zemor [2] gave a modified construction of expander codes, which greatly improves the code parameters. In this paper we present a new simple algebraic decoding algorithm for the modified expander codes of Barg and Zemor, and give a Justesen-type construction of linear-time decodable asymptotically good binary linear codes that meet the Zyablov bound.