Determination of Sizes of Optimal Three‐Dimensional Optical Orthogonal Codes of Weight Three with the AM‐OPP Restriction |
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| Authors: | Lidong Wang Yanxun Chang |
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| Affiliation: | 1. Institute of Mathematics, Beijing Jiaotong University, Beijing, P. R. China;2. Department of Basic Courses, Chinese People's Armed Police Force Academy, Langfang, P. R. China |
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| Abstract: | In this paper, we further investigate the constructions on three‐dimensional  optical orthogonal codes with the at most one optical pulse per wavelength/time plane restriction (briefly AM‐OPP 3D  ‐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 3D  ‐OOC is finally determined for any positive integers  and  . |
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| Keywords: | three‐dimensional optical orthogonal code group divisible packing incomplete group divisible packing holey group divisible design |
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optical orthogonal codes with the at most one optical pulse per wavelength/time plane restriction (briefly AM‐OPP 3D 
‐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 3D 
‐OOC is finally determined for any positive integers 
and 
.