| Because of their own good auto and cross-correlation properties, OOCs are widely used in fiber optic channel CDMA systems. In order to further improve system perfor-mance, S. Kim et al. proposed the concept of three-dimensional optical orthogonal codes(3-D OOCs).A three-dimensional (u×v×w, k,λ) optical orthogonal code (briefly 3-D (u×v× w, k,λ)-OOC),C, is a family of u×v×w(0,1)arrays (called codewords)of Hamming weight k satisfying:for any two arrays A=[a(i, j,l)],B=[b(i, j,l)]∈C and any integer t: where either A≠B or r(?)0 (mod w), and the arithmetic l+τ is reduced modulo w.In this paper, we study constructions of optimal three-dimensional (u×v×w,k,λ) optical orthogonal codes with both at most one pulse per spatial plane (AM-OPPSP) and at most one pulse per wavelength plane (AM-OPPWP) restrictions (briefly AM-OPPS/WP 3-D(u×v×w,k,λ)-OOC).As a result, the necessary and sufficient condi-tions for the existence of a perfect AM-OPPS/WP 3-D(u×v×w,3,1)-OOC are finally determined.This thesis is organized as follows.In Chapter 1,we give a brief introduction on the background of optimal optical orthogonal codes.In Chapter 2, we study optimal AM-OPPS/WP 3-D (u×v×w,k, A)-OOCs. We build an equivalence relation between such an OOC and a certain combinatorial subject, called a w-cyclic group divisible packing of type (u, wv). By this link, the upper bound of the number of codewords is improved and the necessary conditions for the existence of a perfect AM-OPPS/WP 3-D(u×v×w,k,λ)-OOC are determined.In Chapter 3, by this equivalence relation between perfect AM-OPPS/WP 3-D (m×v×w,k,λ)-OOCs and a certain combinatorial subject, called a w-cyclic group divisible design of type (u, wv), we conclude some classical constructions and several new constructions are proposed.In Chapter 4, as an application, the necessary and sufficient conditions for the exis- tence of a perfect AM-OPPS/WP 3-D(u×v×w,3,1)-OOC are completely determined. |
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