  In this paper we introduce a new class of codes for over-loaded synchronous
wireless CDMA systems which increases the number of users for a fixed number of
chips without introducing any errors. In addition these codes support active
user detection. We derive an upper bound on the number of users with a fixed
spreading factor. Also we propose an ML decoder for a subclass of these codes
that is computationally implementable. Although for our simulations we consider
a scenario that is worse than what occurs in practice, simulation results
indicate that this coding/decoding scheme is robust against additive noise. As
an example, for 64 chips and 88 users we propose a coding/decoding scheme that
can obtain an arbitrary small probability of error which is computationally
feasible and can detect active users. Furthermore, we prove that for this to be
possible the number of users cannot be beyond 230.
