The paper deals with the multi-user detection in the context of random permutations. Random permutations, as a special class of discrete linear periodic time varying filters, are a tool to generate multiple access, for which it is important to develop appropriate receiver detectors. The case of the synchronous model is considered, for which two detectors are developed: the matched-filter detector and the decorrelating detector. Theoretical probabilities of error are given, which are confirmed by Monte-Carlo simulations. A comparison with decorrelating techniques for CDMA systems is provided, along with a discussion on the choice of the permutations.