The paper presents a random spreading code assignment scheme for enhancing channel efficiency in centralized DS-SS packet radio networks which employ a multiple-capture receiver for each code channel. Compared to the common code case, this approach requires a modest increase in receiver complexity, but the number of distinct spreading codes being used is considerably less than the number of radios in the network. A general theoretical framework for evaluation of collision-free packet performance in each code channel is described, in which the possibility of collision-free transmission is conservatively estimated using a combinatorial method, and the effects of asynchronous multiple-access interference are characterized in terms of the primary and secondary user interferences. At the link level, the capture and throughput performances are evaluated for a proper set of codes, and compared with the results from the common code scheme. It is shown that the use of a random assignment scheme with more than one code results in a higher performance gain, and most of this gain can be achieved with just two distinct spreading codes.< >