2-dimensional optical orthogonal codes from singer groups

We present several new families of (Λ×T,w,λ)(Λ×T,w,λ) (2D) wavelength/time optical orthogonal codes (2D-OOCs) with λ=1,2λ=1,2. All families presented are either optimal with respect to the Johnson bound (JJ-optimal) or are asymptotically optimal. The codes presented have more flexible dimensions and weight than the JJ-optimal families appearing in the literature. The constructions are based on certain pointsets in finite projective spaces of dimension kk over GF(q)GF(q) denoted PG(k,q)PG(k,q). This finite geometries framework gives structure to the codes providing insight. We establish that all 2D-OOCs constructed are in fact maximal (in that no new codeword may be added to the original whereby code cardinality is increased).