Optimal three-dimensional optical orthogonal codes of weight three

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.

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