Constructions of Optimal 2-D Optical Orthogonal Codes via Generalized Cyclotomic Classes

Optical orthogonal codes (OOCs) are widely used as spreading codes in optical fiber networks. In this paper, a bound on the code size of 2-D OOCs with both at most one-pulse per wavelength (AM-OPPW) and at most one-pulse per time slot (AM-OPPTS) is derived. Accordingly, two constructions of optimal 2-D OOCs with both AM-OPPW and AM-OPPTS are proposed via the generalized cyclotomic classes. Furthermore, optimal 2-D OOC with AM-OPPW can be also constructed by adding more codewords into the 2-D OOCs with both AM-OPPW and AM-OPPTS.