Pseudorandom sequences with low autocorrelation magnitude play important roles in various environments. Let N be a prime with N=Mf+1, where M and f are positive integers. A new method to construct M-sequences of period 4N is given. We show that these new sequences have low autocorrelation magnitude.

In this letter, we enumerate the number of cyclically inequivalent M-ary Sidel'nikov sequences of given length as well as the number of distinct autocorrelation distributions that they can have, while we change the primitive element for generating the sequence.