The use of partial geometries to construct parity-check matrices for LDPC codes has
resulted in the design of successful codes with a probability of error close to the Shannon
capacity at bit error rates down to $10^{-15}$. Such considerations have motivated this
further investigation. A new and simple construction of a type of partial geometries with
quasi-cyclic structure is given and their properties are investigated. The trapping sets of
the partial geometry codes were considered previously using the geometric aspects of the
underlying structure to derive information on the size of allowable trapping sets. This
topic is further considered here. Finally, there is a natural relationship between partial
geometries and strongly regular graphs. The eigenvalues of the adjacency matrices of such
graphs are well known and it is of interest to determine if any of the Tanner graphs
derived from the partial geometries are good expanders for certain parameter sets, since it
can be argued that codes with good geometric and expansion properties might perform well
under message-passing decoding.