New \(M\)-ary sequences with low autocorrelation from interleaved technique
Let \(p\) and \(q\) be two odd primes with \(p=Mf+1\) and \(M\) is even. A new construction of \(M\)-ary sequences of period \(pq\) with low periodic autocorrelation is presented in this paper based on interleaving the \(M\)-ary power residue sequence of period \(p\) according to the quadratic residue with respect to \(q\). This construction can generate the well-known twin-prime sequence and generalized cyclotomy sequence of order two if \(M=2\). For \(M=4\), a new class of quaternary sequences of period \(pq\) with maximal nontrivial autocorrelation value being either \(\sqrt{5}\) or \(3\) is obtained. This achieves the best known results for such kind of quaternary sequences.
\(m\)-ary sequence autocorrelation interleaved structure low correlation 94a05 94a55