In this paper a method calculates the time offset between a binary sequence and its shifted sequence based on the number theoretic approach is presented. Using this method the time offset between a binary sequence and its shifted sequence can be calculated. It has been recongnized that the defining the reference (zero-offset) sequence is important in synchronous code division multiple access(CDMA) system since the same spreading sequence are used by the all base station. The time offset of the sequence with respect to the zero offset sequence are used to distinguish signal received at a mobile station from different base stations. This paper also discusses a method that defines the reference sequence.