Geometric constructions of optimal optical orthogonal codes

We provide a variety of constructions of (n,w, λ)-optical orthogonal codes using special sets of points and Singer groups in finite projective spaces. In several of the constructions, we are able to prove that the resulting codes are optimal with respect to the Johnson bound. The optimal codes exhibited have λ = 1, 2 and w − 1 (where w is the weight of each codeword in the code). The remaining constructions are are shown to be asymptotically optimal with respect to the Johnson bound, and in some cases maximal. These codes represent an improvement upon previously known codes by shortening the length. In some cases the constructions give rise to variable weight OOCs.