  Finite field transforms are offered as a new tool of spreading sequence
design. This approach exploits orthogonality properties of synchronous
non-binary sequences defined over a complex finite field. It is promising for
channels supporting a high signal-to-noise ratio. New digital multiplex schemes
based on such sequences have also been introduced, which are multilevel Code
Division Multiplex. These schemes termed Galois-field Division Multiplex (GDM)
are based on transforms for which there exists fast algorithms. They are also
convenient from the hardware viewpoint since they can be implemented by a
Digital Signal Processor. A new Efficient-bandwidth
code-division-multiple-access (CDMA) is introduced, which is based on
multilevel spread spectrum sequences over a Galois field. The primary advantage
of such schemes regarding classical multiple access digital schemes is their
better spectral efficiency. Galois-Fourier transforms contain some redundancy
and only cyclotomic coefficients are needed to be transmitted yielding compact
spectrum requirements.
