Constructions of two-dimensional optical orthogonal codes of weight three

The study of optical orthogonal codes has been motivated by an application in an optical code-division multiple access system. This paper focuses on optimal two-dimensional optical orthogonal codes with auto-correlation and cross-correlation both equal to 1. By examining the structures of n -cyclic group divisible packings and semi-cyclic incomplete holey group divisible designs, we present new combinatorial constructions for two-dimensional ( 𝑚 × 𝑛 , 𝑘 , 1 ) -optical orthogonal codes. As a consequence, the exact number of codewords of an optimal two-dimensional ( 𝑚 × 𝑛 , 3 , 1 ) -optical orthogonal code is determined for any positive integers m and n .