LAUSR

The study of optical orthogonal codes has been motivated by an application in an optical code-division multiple access system. From a practical point of view, compared to one-dimensional optical orthogonal codes, two-dimensional optical orthogonal codes tend to require smaller code length. On the other hand, in some circumstances only with good cross-correlation one can deal with both synchronization and user identification. These motivate the study of two-dimensional optical orthogonal codes with better cross-correlation than auto-correlation. This paper focuses on optimal two-dimensional optical orthogonal codes with the auto-correlation λa and the best cross-correlation 1. By examining the structures of w-cyclic group divisible designs and semi-cyclic incomplete holey group divisible designs, we present new combinatorial constructions for two-dimensional (n×m,k,λa,1)-optical orthogonal codes. When k=3 and λa=2, the exact number of codewords of an optimal two-dimensional (n×m,3,2,1)-optical orthogonal code is determined for any positive integers n and m≡2(mod4).