If the period of anm-sequence is2^t - 1 = n_1 n_2withn_1relative prime ton_2, then the vectorm, a period of them-sequence, can be decomposed in a special way into two subsequences of lengthsn_1andn_2. The properties and structures of them-sequence and its subsequences are studied under such decomposition. The following applications are direct consequences. The correlation technique for the detection ofm- sequences can be improved. The weight distributions of a class of cyclic codes can be easily obtained. A scheme for improving the feedback communication is developed. And a method for designing cyclic codes with desirable weights is suggested.