This paper studies the joint detection of bits for a new spread-spectrum system based on random permutations. The proposed technique can be regarded as a special case of discrete linear periodic time varying filters. As any spread-spectrum technique, this method generates multi-access interference, which must be mitigated in order to retrieve the users' bits with acceptable bit-error-rate. Thus, different detection strategies must be analysed regarding their performance, their complexity and the available a priori information. In this paper, an asynchronous model is considered, and a linear minimum mean-square error (MMSE) detector fitted to this model is investigated. Theoretical and simulated results are provided, along with a comparison with the corresponding detector for CDMA systems.