Generation of code sequences for asynchronous optical CDMA systems

In this paper two families of optical orthogonal codes (OOCs) are algebraically designed by using the Galois field. The first family of codes has nonideal auto band cross-correlation λ_a=1, λ_c=2 properties. The second family of codes has ideal auto band cross-correlation λ_a=1, λ_c=1 properties. It is shown that the p-1 codes exist for every prime p forming a family of (v, ω, λ_a, λ_c) OOCs. These codes may serve as many as p-1 different users in the fiber-optic code division mutiple access system. We also compare their performance with previous known codes. We present examples of the constructed codes. The algebraic OOCs being proposed in this paper find applications in asynchronous OCDMA systems.