A special coding scheme is disclosed for more effectively acquiring a long code and frame timing during a cell search in a CDMA communications system. A code set of length M Q-ary code words including symbols from a set of Q short codes is defined with certain properties. The primary property to be satisfied is that no cyclic shift of a code word yields a valid code word. The other properties to be satisfied are that there is a one-to-one mapping between a long code message and a valid code word, and a decoder should be able to find both the random shift (thereby implicitly finding the frame timing) and the transmitted code word (i.e., its associated long code indication message) in the presence of interference and noise, with some degree of accuracy and reasonable complexity.