I. Introduction
Optical code-division multiple access (OCDMA) has been recently receiving renewed attention because of the advancement of two-dimensional (2-D), such as wavelengthhopping time-spreading (or so-called wavelength-time), coding technologies [1]–[8]. In particular, the basic idea of the wavelength–time coding scheme is first to spread a broad-band short laser pulse into pulses of different wavelengths by a wavelength-demultiplexing device, then to perform coding by controlling the amplitudes and time delays of these pulses, and finally to recombine the coded pulses by a wavelength-multiplexing device [5], [6], [8]–[15]. Classes of 2-D codes that can be used as wavelength–time codes have also been studied [2]–[4], [6] [7] [8], [16]–[22]. Wavelength–time codes increase the numbers of subscribers and simultaneous users by utilizing two coding dimensions simultaneously, rather than by using only one coding dimension, namely time, in the well-known prime codes and optical orthogonal codes [7], [23], [24], or namely wavelength, in the -sequences and Walsh code [14], [15], [25] [26] [27].