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, λ_a, λ_c)-OOC with size L is a family of L {0,1}-sequences with length N, weight w, maximum autocorrelation λ_a, and maximum cross correlation λ_c. In this paper, we present two new constructions for OOCs with λ_a=λ_c=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 Z_pⁿ, 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...p_k, M, 1,1)-OOC with size (p₁...p_k-1)/M from a product of k finite fields, where p_i is an odd prime and M is a positive integer such that M| p_i-1 for 1 ≤ i ≤ k. In particular, it is optimal in the case that k=1 and (M-1)² > p₁-1.