Optimal optical orthogonal signature pattern codes with weight three and cross-correlation constraint one

Optical orthogonal signature pattern codes (OOSPCs) have attracted wide attention as signature patterns of spatial optical code division multiple access networks. In this paper, an improved upper bound on the size of an $(m,n,3,{\lambda }_a,1)$-OOSPC with ${\lambda }_a=2,3$ is established. The exact number of codewords of an optimal $(m,n,3,{\lambda }_a,1)$-OOSPC is determined for any positive integers $m,n\equiv 2(\mathrm{m}\mathrm{o}\mathrm{d}4)$ and ${\lambda }_a\in \{2,3\}$.