Decimation of m-sequences leading to any desired phase shift

If every kth bit of an m-sequence A of periodicity 2n ¿ 1 is sampled, where (k, 2n ¿ 1) = 1, the resultant sequence A(k) is also an m-sequence with the same periodicity. The dependence between the first n bits of A and those of A(k) is shown here. For k = 2m, A(k) is a shifted version of A. It si also shown how the n-tuple is to be determined with which A should start in order that the phase shift between A and A(k) should be q,0 ¿ q ¿ 2n ¿ 2.