To further enhance code cardinality and coding flexibility, a third coding dimension can be added to 2-D optical codes, resulting in 3-D optical codes [1–6]. In this chapter, 3-D concatenated prime codes and multicarrier prime codes are studied [1, 3, 4], in which the third coding dimension is supported by multiple spatial, fiber-optic, or wavelength-band channels.
The 2-D carrier-hopping prime codes over GF(p) in Section 5.1 can be treated as wavelength-time matrices of pulses in distinct wavelengths and time slots. This property gives zero autocorrelation sidelobes and periodic cross-correlation functions of at most 1. Nevertheless, the construction cannot be used with any extension field ...
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