New constructions of asymptotically optimal optical orthogonal codes with λ = 1

Abstract

Optical orthogonal codes (OOCs) are widely used as spreading codes in optical fiber networks. For reliable and efficient data transmission in these systems, it is required to design OOCs with low correlation and large size. In this paper, we present two new constructions for asymptotically optimal OOCs with respect to the Johnson bound, whose maximum nontrivial correlation value is 1. We first construct an asymptotically optimal OOC of length (p − 1)p 2 for an odd prime p by using the structure of the ring of integers modulo p 2 . We then present an asymptotically optimal OOC of length Mp1p2 from a product of two finite fields, where p1 and p2 are odd primes, and M is an integer such that M | pi − 1 for i = 1, 2.Index Terms-Correlation, optical fiber networks, finite fields, ring of integers modulo n, optical orthogonal codes (OOCs).