Abstract
M-sequences generated by a feedback shift register are frequently used as a binary random number. When an N-th order M-sequence is generated repeatedly, it is necessary to initialize the state of an N-stage shift register so that the subsequence of the M-sequence has good random property for the length 2n(n<N).
This paper first defines n-th order random sequences with the length 2n, and deduces the n-th order ideal random sequences whose subsequences for the length 2n, 2n-2, 2n-4, …, etc. become the random sequences of order n, (n-2), (n-4), …, respectively. Secondly, the initialization procedure of the high order M-sequence is investigated in order to approximate the M-sequence to an ideal random sequence as closely as possible. It is shown that [log2N]-th order ideal random sequences are suitable for the initial values of the N-th order M-sequence in order for the M-sequence to look like an ideal random sequence.
