n-dimensional optical orthogonal codes, bounds and optimal constructions

We generalize to higher dimensions the notions of optical orthogonal codes. We establish upper bounds on the capacity of general n-dimensional OOCs, and on ideal codes (codes with zero off-peak autocorrelation). The bounds are based on the Johnson bound, and subsume bounds in the literature. We also present two new constructions of ideal codes; one furnishes an infinite family of optimal codes for each dimension n >= 2, and another which provides an asymptotically optimal family for each dimension n >= 2. The constructions presented are based on certain point-sets in finite projective spaces of dimension k over GF(q) denoted PG(k, q).