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Optimal three-dimensional optical orthogonal codes of weight three

机译：权重3的最佳三维光学正交码

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摘要

Using polarization technique in optical code division multiple access, we can schedule the transmission of optical pulses in spatial domain, in addition to the frequency domain and time domain. An optical orthogonal code (OOC) which spreads in these dimensions is called a three-dimensional (3-D) OOC. In this paper, we study 3-D OOC with at most one optical pulse per wavelength/time plane, which have the favorable property that the Hamming auto-correlation is identically equal to 0. An upper bound on the number of codewords for general Hamming cross-correlation requirement is given. A 3-D OCC with at most one pulse per wavelength/time plane and Hamming cross-correlation no more than 1 is shown to be equivalent to a generalized Bhaskar Rao group divisible design (GBRGDD), signed over a cyclic group. Through this equivalence, necessary and sufficient conditions for the existence of GBRGDD of weighted 3, signed over a cyclic group, are derived.
机译：在光码分多址中使用偏振技术，除了频域和时域外，我们还可以在空间域中调度光脉冲的传输。在这些维度上扩展的光学正交码（OOC）被称为三维（3-D）OOC。在本文中，我们研究每个波长/时间平面最多具有一个光脉冲的3-D OOC，其具有的良好特性是汉明自相关等于0。通用汉明码字数的上限给出了互相关要求。具有每个波长/时间平面最多一个脉冲且汉明互相关不大于1的3-D OCC等效于在循环组上签名的广义Bhaskar Rao组可分设计（GBRGDD）。通过这种等效，得出存在于环状基团上的权重3的GBRGDD的充要条件。

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