LDPC codes generated by conics in the classical projective plane

We construct various classes of low-density parity-check codes using point-line incidence structures in the classical projective plane PG(2, q). Each incidence structure is based on the various point classes (internal, external) and line classes (skew, tangent, secant) created by the geometry of a conic in the plane. For each class, we prove various properties about dimension and minimum distance. Some arguments involve the geometry of two conics in the plane. As a result, we prove, under mild conditions, the existence of two conics, one entirely internal (or external) to the other. AMS Classification: 51E22, 94B05