A new family of ternary sequences with ideal two-level autocorrelation function (Q5937083)

The authors construct a new family of ternary sequences \(\{s(t)\}\) with two-level autocorrelation function. They are defined by \[ s(t)=\text{Tr}_n(\alpha^t+\alpha^{dt}), \] where \(\alpha\) is a primitive element of \(\text{GF}(3^n)\), \(n=3k\) and \(d=3^{2k}-3^k+1.\) The sequences have period \(3^n-1\), and they are balanced in the sense that each of the elements 1 and 2 occurs \(3^{n-1}\) times during a period of the sequence.