No abstract

No abstract

No abstract

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 wavelength/time plane restriction (briefly AM-OPP 3-D (u × v × w, k, 1)-OOCs) by way of the corresponding designs. Several new auxiliary designs such as incomplete holey group divisible designs and incomplete group divisible packings are introduced and therefore new constructions are presented. As a consequence, the exact number of codewords of an optimal AM-OPP 3-D (u × v × w, 3, 1)-OOC is finally determined for any positive integers v, w and u ≥ 3.