Decomposition of M-sequences and its applications

If the period of an
m
-sequence is
2^t - 1 = n_1 n_2
with
n_1
relative prime to
n_2
, then the vector
m
, a period of the
m
-sequence, can be decomposed in a special way into two subsequences of lengths
n_1
and
n_2
. The properties and structures of the
m
-sequence and its subsequences are studied under such decomposition. The following applications are direct consequences. The correlation technique for the detection of
m
- 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.