Constructions of Optical Orthogonal Codes from Finite Geometry

The link between finite geometry and various classes of error-correcting codes is well known. Arcs in projective spaces, for instance, have a close tie to linear MDS codes as well as the high-performing low-density parity-check codes. In this article, we demonstrate a connection between arcs and optical orthogonal codes (OOCs), a class of nonlinear binary codes used for many modern communication applications. Using arcs and Baer subspaces of finite projective spaces, we construct some infinite classes of OOCs with auto-correlation and cross-correlation both larger than 1.