Asymptotically Optimal Optical Orthogonal Codes With New Parameters

Optical orthogonal codes (OOCs) are widely used as spreading codes in optical fiber networks. An (N, w, λa, λc)-OOC with size L is a family of L {0,1}-sequences with length N, weight w, maximum autocorrelation λa, and maximum cross correlation λc. In this paper, we present two new constructions for OOCs with λa=λc=1 which are asymptotically optimal with respect to the Johnson bound. We first construct an asymptotically optimal (Mpn, M, 1,1)-OOC with size (pn-1)/M by using the structure of Zpn, the ring of integers modulo pn, where p is an odd prime with M|p-1, and n is a positive integer. We then present another asymptotically optimal (Mp1...pk, M, 1,1)-OOC with size (p1...pk-1)/M from a product of k finite fields, where piis an odd prime and M is a positive integer such that M| pi-1 for 1 ≤ i ≤ k. In particular, it is optimal in the case that k=1 and (M-1)2> p1-1.