Algebraic constructions of low-density parity-check (LDPC) codes are important for code designing because of their implementation advantages and properties that facilitate their analysis. This thesis presents a concise notation for LDPC codes that are constructed using a two-step circulant covering process. By implementing this process, instead of a single circulant cover, we are able to show improved minimum distance and girth properties. These improvements were verified by results from codes constructed from a two-step circulant cover of the 2 x 3 complete bipartite graph.
