Classes of optical orthogonal codes from arcs in root subspaces

We present new constructions for (n,w,λ)(n,w,λ) optical orthogonal codes (OOC) using techniques from finite projective geometry. In one case codewords correspond to (q-1)(q-1)-arcs contained in Baer subspaces (and, in general, kkth-root subspaces) of a projective space. In the other construction, we use sublines isomorphic to PG(2,q)PG(2,q) lying in a projective plane isomorphic to PG(2,qk)PG(2,qk), k>1k>1. Our construction yields for each λ>1λ>1 an infinite family of OOCs which, in many cases, are asymptotically optimal with respect to the Johnson bound.