Classes of optical orthogonal codes from arcs in root subspaces

Abstract

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