Finite field transforms are offered as a new tool of spreading sequence design. This approach exploits orthogonality
roperties 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 exist 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.