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Orthogonal variable spreading factor (OVSF) codes have been proposed as the channelization codes used in the wideband CDMA access technology of IMT-2000. OVSF codes have the advantage of supporting variable bit rate services, which is important to emerging multimedia applications. The objective of OVSF code assignment algorithm is to minimize the probability of code request denial due to inappropriate resource allocation. In this paper, we propose an efficient OVSF code assignment scheme that utilizes multiple Rake combiners in user equipments. Our approach finds in constant time all feasible codewords for any particular request, trying to minimize both rate wastage and code fragments. The simulation result shows that our scheme outperforms previous work in the probability of request denial. The code management overhead is also minimal in our scheme.