具有AM-OPP约束的最优三维光正交码码长的确定
Determination of sizes of optimal three-dimensional optical orthogonal codes of weight three with the AM-OPP restriction
摘要：
本文通过相应的设计，进一步研究了每个波长/时间平面至多一个光脉冲的三维$(u\times v\times w,k,1)$光正交码（简称AM-$3$-D $(u\times v\times w,k,1)$ -OOCs）的构造.引入了一些新的辅助设计，如不完全多孔群可分设计和不完全群可分填充，从而给出了新的构造。结果，对于任何正整数$v,w$和$u\geq3$，最终确定最佳AM-$3$-D $(u\times v\times w,3,1)$ -OOC的码字的确切数目。
英文摘要：
In this paper, we further investigate the constructions on three-dimensional $(u\times v\times w,k,1)$ optical orthogonal codes with the at most one optical pulse per wavelength/time plane restriction (briefly AM-OPP $3$-D $(u\times v\times w,k,1)$-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 $(u\times v\times w,3,1)$-OOC is finally determined for any positive integers $v,w$ and $u\geq3$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
