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In this paper, we are concerned about optimal two-dimensional opticalorthogonal codes with $\lambda$ = 2. Some combinatorial constructions arepresented and many infinite families of optimal two-dimensional opticalorthogonal codes with weight 4 and $\lambda$ = 2 are obtained. Especially, weshall see that in many cases an optimal two-dimensional optical orthogonal codecan not achieve the Johnson bound.

Combinatorial constructions for optimal two-dimensional optical orthogonal codes with $\lambda$ = 2