We provide a new construction yielding one new and one known infinite family of optimal (n,w,2) -optical orthogonal codes,wisin {4,6}. Our construction relies on various techniques in finite projective spaces involving hyperovals in projective planes and Singer groups.

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.

We study certain projections of binary linear codes onto larger fields. These projections include the well-known projection of the extended Golay [24,12,8] code onto the hexacode over $\mbox{GF}(4)$ and the projection of the Reed--Muller code R(2,5) onto the unique self-dual [8,4,4] code over $\mbox{GF}(4)$. We give acharacterization of these projections, and we construct several binary linear codes which have best known optimal parameters, for instance, [20,11,5], [40,22,8], [48,21,12], and [72,31,16]. We also relate the automorphism group of a quaternary code to that of the corresponding binary code.