New construction of asymptotically optimal optical orthogonal codes

Abstract

An optical orthogonal code (OOC) of length N is a set of {0, 1}-sequences of length N, all of which have a constant weight. It is employed as a spreading code in optical communication systems, where 1 means signal `on' and 0 signal `off.' In this paper, we present a generic construction of OOCs of length (q-1)N from an OOC of length N, where q is a prime power with gcd(q -1,N) = 1. This construction can be applied to any OOCs with maximum correlation value 1 and weight less than or equal to q. As a result, a new family of asymptotically optimal OOCs with respect to the Johnson bound can be obtained from an optimal OOC with maximum correlation value 1.