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Decomposition of M-sequences and its applications

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1 Author(s)

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.

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IEEE Transactions on Information Theory  (Volume:17 ,  Issue: 4 )