Determination of sizes of optimal three-dimensional optical orthogonal codes of weight three with the AM-OPP restriction

In this paper, we further investigate the constructions on three-dimensional(u × v × w, k, 1) optical orthogonal codes with the at most one optical pulse per wave-length/time plane restriction (briefly AM-OPP 3-D (u × v × w, k, 1)-OOCs) by way ofthe corresponding designs. Several new auxiliary designs such as incomplete holey groupdivisible designs and incomplete group divisible packings are introduced and thereforenew constructions are presented. As a consequence, the exact number of codewords ofan optimal AM-OPP 3-D (u × v × w, 3, 1)-OOC is finally determined for any positiveintegers v,w and u ≥ 3.