Divisible difference sets, relative difference sets and sequences with ideal autocorrelation

In this correspondence, we consider the equivalent condition that a sequence possesses ideal autocorrelation function. As we know, for a binary sequence, the equivalent condition is that the characteristic class of this sequence consists of two cyclic difference sets. This paper proves that, for a p-ary sequence with d-form property, the equivalent condition is that its characteristic class consists of one cyclic divisible difference sets and p − 1 relative difference sets. Moreover, a new way to construct cyclic divisible difference sets is presented.