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This paper focuses on multiuser detection for multicarrier code-division multiple-access (MC-CDMA) systems, employing cyclic-prefixed (CP) or zero-padded (ZP) transmission techniques. For both systems, we consider either the classical linear finite-impulse response (L-FIR) receiving structures or, when the transmitted symbols are improper, the proposed widely linear FIR (WL-FIR) ones, which process both the received signal and its complex-conjugate version. With regard to both CP- and ZP-based downlink configurations, it is shown that, if the number of users does not exceed a given threshold and their codes are appropriately designed, L-FIR and WL-FIR universal zero-forcing (ZF) multiuser detectors can be synthesized, which, in the absence of noise, guarantee perfect symbol recovery for each user, regardless of the underlying frequency-selective channel. In particular, some spreading code examples are provided, which satisfy the design rules. Finally, numerical simulations are carried out to show that the theoretical considerations developed herein provide useful guidelines for practical MC-CDMA system designs.