In dense passive radio frequency identification (RFID) systems, code division multiple access (CDMA) techniques can be used to alleviate severe collisions and thus enhance the system performance. However, conventional CDMA techniques are challenging to implement, especially for passive tags due to cost and power constraints. In this paper, we design a CDMA-based multi-reader passive ultra high frequency (UHF) RFID system in which a reader detects only the strongest tag signal and a tag uses Gold codes only on the preamble and the data bits of RN16 without increasing its clock frequency. We present a new communication procedure based on dynamic framed slotted ALOHA (DFSA). In order to optimize the system, we theoretically analyze the system performance in terms of slot capacity and identification rate, and formally show how the code length and the number of readers affect the identification rate. Furthermore, we propose an effective method for tag estimation and frame size adjustment, and validate it via simulations. Through an example, we demonstrate how the analysis-based technique can be used to optimize the system configurations with respect to the number of readers and the number and length of Gold codes.