Asymptotically optimal optical orthogonal codes with new parameters

Abstract

Optical orthogonal codes (OOCs) are widely used as spreading codes in optical fiber networks. An (N,w,λa,λ c)-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 left(Mp^{n},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 (p1p k-1)/M from a product of k finite fields, where pi is 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.