Construction of Space/Wavelength/Time Spread Optical Code with Large Family Size

Using two kinds of combinatorial designs, namely orthogonal array and r-simple matrix, as building blocks, a novel construction for three-dimensional single-pulse-per-plane codes (3-D SPPCs), spreading over space, wavelength and time, is presented. The new construction is more flexible than existing constructions. In the literature, previously presented constructions of 3-D SPPCs have maximum Hamming cross-correlation equal to one. The new constructions can have maximal Hamming cross-correlation larger than or equal to one. By comparing with an upper bound on the number of codewords, it is shown that some of the 3-D SPPCs obtained by this construction are asymptotically optimal.