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We consider the problem of cognitive code-division channelization (simultaneous power and code-channel allocation) for secondary transmission links co-existing with an unknown primary code-division multiple-access (CDMA) system. We first develop a blind primary-user identification scheme to detect the binary code sequences (signatures) utilized by primary users. To create a secondary link we propose two alternative procedures -one of moderate and one of low computational complexity- that optimize the secondary transmitting power and binary code-channel assignment in accordance with the detected primary code channels to avoid "harmful" interference. At the same time, the optimization procedures guarantee that the signal-to-interference-plus-noise ratio (SINR) at the output of the maximum SINR linear secondary receiver is no less than a certain threshold to meet secondary transmission quality of service (QoS) requirements. The extension of the channelization problem to multiple secondary links is also investigated. Simulation studies presented herein illustrate the theoretical developments.