The even-odd transform (EOT) converts a complex sequence set into another one with even and odd correlation distributions exchanged. The Fukumasa-Kohno-Imai transform (FKIT) converts a real-valued sequence set into a complex one with improved generalized even-odd-equivalent (EOE) correlation distributions. In this work, the EOT is generalized for asynchronous M-PSK/CDMA. A subclass of the generalized EOTs coincides with the FKITs. New bounds on the correlation gains achievable by the FKITs are then derived.