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

In this paper, we are concerned about optimal two-dimensional optical orthogonal codes with $\lambda$ = 2. Some combinatorial constructions are presented and many infinite families of optimal two-dimensional optical orthogonal codes with weight 4 and $\lambda$ = 2 are obtained. Especially, we shall see that in many cases an optimal two-dimensional optical orthogonal code can not achieve the Johnson bound.Comment: This is our paper published by IEEE Transactions on Information Theory in 2011. The paper is too long to be readable in the IEEE version, so we edited it again, but the content is the sam