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 (Mp
ⁿ
, M, 1,1)-OOC with size (p
ⁿ
-1)/M by using the structure of Z
_p
ⁿ
, the ring of integers modulo p
ⁿ
, where p is an odd prime with M|p-1, and n is a positive integer. We then present another asymptotically optimal (Mp
₁
...p
_k
, M, 1,1)-OOC with size (p
₁
...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
> p
₁
-1.