We construct two families of low-density parity-check codes using point-line incidence structures in PG (3 ,q ). The selection of lines for each structure relies on the geometry of the two classical quadratic surfaces in PG (3, q ), the hyperbolic quadric and the elliptic quadric.

Author Bio

We are both senior Mathematics majors at the University of Mary Washington, both originally from Midlothian, Virginia. We worked in the field of Error-Correcting codes during a 10 week Summer Science research program at the University of Mary Washington under the supervision of Dr. Keith Mellinger. We plan to continue research in this area through independent studies in the Fall and Spring. We are both also considering graduate studies in Mathematics when we graduate in the Spring of 2005.