Optimal 2-D (n x m, 3, 2, 1)-optical Orthogonal Codes

Optical orthogonal codes are commonly used as signature codes for optical code-division multiple access systems. So far, research on 2-D optical orthogonal codes has mainly concentrated on the same autocorrelation and cross-correlation constraints. In this paper, we are concerned about optimal 2-D optical orthogonal codes with the autocorrelation lambda(a) and the cross-correlation 1. Some combinatorial constructions for 2-D (n x m, k, lambda(a), 1-optical orthogonal codes are presented. When k = 3 and lambda(a) = 2, the exact number of codewords of an optimal 2-D (n x m, 3, 2, 1)-optical orthogonal code is determined for any positive integers n equivalent to 0, 1, 3, 6, 9, 10 (mod 12) and m equivalent to 2 (mod 4).