M-sequences have several properties that make them attractive for spread spectrum applications they are:

• Property 1: An m-sequence has 2n - 1 ones and 2n - 1 - 1 zeros.
• Property 2: If we slide a window of length n along the output sequence for N shifts, where N = 2n - 1, each n-tuple, except the all-zero sequence, appears exactly once.
• Property 3:There is one run of ones of length n; one run of zeros of length n - 1; one run of ones and one run of zeros of length n - 2; two runs of ones and two runs of zeros of length n - 3; and, in general, 2Yi -3 runs of ones and 2n - 3 runs of zeros of length 1.

For many communications applications, the 0, 1 sequence is changed to a ±1 sequence by representing a binary 1 with 1 and a binary ° with -1.5 We define the periodic autocorrelation of the resulting sequences as

• Property 4: The periodic autocorrelation of a ± 1 m-sequence is