LDPC Codes from Triangle-Free Line Sets

We study sets of lines of AG(n, q) and PG(n, q) with the property that no three lines form a triangle. As a result the associated point-line incidence graph contains no 6-cycles and necessarily has girth at least 8. One can then use the associated incidence matrices to form binary linear codes which can be considered as LDPC codes. The relatively high girth allows for efficient implementation of these codes. We give two general constructions for such triangle-free line sets and give the parameters for the associated codes when q is small.