Combinatorial Constructions for Optimal Two-Dimensional Optical Orthogonal Codes

Optical orthogonal codes (OOCs) have been designed for OCDMA. A one-dimensional (1-D) optical orthogonal code (1-D OOC) is a set of one-dimensional binary sequences having good auto and cross-correlations. One limitation of 1-D OOC is that the length of the sequence increases rapidly when the number of users or the weight of the code is increased, which means large bandwidth expansion is required if a big number of codewords is needed. To lessen this problem, two-dimensional (2-D) coding (also called multiwavelength OOCs) was invested. A two dimensional (2-D) optical orthogonal code (2-D OOC) is a set of utimesv matrices with (0, 1) elements having good auto and cross-correlations. Recently, many researchers are working on constructions and designs of 2-D OOCs. In this paper, we shall reveal the combinatorial properties of 2-D OOCs and give an equivalent combinatorial description of a 2-D OOC. Based on this, we are able to use combinatorial methods to obtain many optimal 2-D OOCs.