Combinatorial constructions for optimal 2-D optical orthogonal codes with AM-OPPTS property

We develop a new one-to-one correspondence between a two-dimensional ( m × n , k , ρ ) optical orthogonal code (2-D ( m × n , k , ρ )-OOC) with AM-OPPTS (at most one-pulse per time slot) property and a certain combinatorial subject, called an n -cyclic holey packing of type m n . By this link, an upper bound on the size of a 2-D ( m × n , k , ρ )-OOC with AM-OPPTS property is derived. Afterwards, we employ combinatorial methods to construct infinitely many 2-D ( m × n , k , 1)-OOCs with AM-OPPTS property, whose existence was previously unknown. All these constructions meet the upper bounds with equality and are thus optimal.