Derivation of autocorrelation distributions of Sidel´nikov sequences using cyclotomic numbers

In this paper, we derived the autocorrelation distributions, i.e., the values and the number of occurrences of each value of the autocorrelation function of Sidel´nikov sequences. The frequency of each autocorrelation value of an M-ary Sidel´nikov sequence is expressed in terms of the cyclotomic numbers of order M. It is also pointed out that the total number of distinct autocorrelation values is dependent not only on M but also on the period of the sequence, but always less than or equal to (₂ ^M) + 1