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The use of partial geometries to construct parity-check matrices for LDPCcodes has resulted in the design of successful codes with a probability oferror close to the Shannon capacity at bit error rates down to $10^{-15}$. Suchconsiderations have motivated this further investigation. A new and simpleconstruction of a type of partial geometries with quasi-cyclic structure isgiven and their properties are investigated. The trapping sets of the partialgeometry codes were considered previously using the geometric aspects of theunderlying structure to derive information on the size of allowable trappingsets. This topic is further considered here. Finally, there is a naturalrelationship between partial geometries and strongly regular graphs. Theeigenvalues of the adjacency matrices of such graphs are well known and it isof interest to determine if any of the Tanner graphs derived from the partialgeometries are good expanders for certain parameter sets, since it can beargued that codes with good geometric and expansion properties might performwell under message-passing decoding.

New Classes of Partial Geometries and Their Associated LDPC Codes