Low-density parity-check codes based on finite geometries: a rediscovery and new results
IEEE Transactions on Information Theory
LDPC codes generated by conics in the classical projective plane
Designs, Codes and Cryptography
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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 that 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.