Beyond-3G wireless communication systems should support various types of packet traffic with both low/medium and high rates. However, scheduling-based resource allocation schemes and dedicated resource allocation/multiplexing schemes are inadequate for accommodating low/medium rate services due to a rate mismatch, a large signaling overhead, and an inefficient usage of radio resources. Therefore, a new orthogonal frequency and code hopping multiplexing~(OFCHM) scheme for downlink multiplexing is proposed to provide efficient support of packet traffic with low and medium data rates in a spread OFDM environment. The performance of the proposed scheme is evaluated in terms of the statistical multiplexing gain, the block error rate, and the overall capacity by using both an analytical approach and simulation. A comparison study with the VSF-OFCDM system through system-level simulations is also performed. Two synergy/perforation control schemes for M-QAM are proposed, and the multi-rate transmission is generalized in OFCHM. The proposed synergy/perforation control schemes are evaluated through an analytical approach and simulations, and are compared to the previous scheme for QPSK modulation. The resource-collision probability is analyzed in the generalized multi-rate environment, and the analytical results are compared with simulation ones.