Constructions of quaternary sequences with ideal autocorrelation. (Chinese. English summary) Zbl 1313.94041
Summary: For an arbitrary binary sequence of odd period \(p\) with optimal autocorrelation, quaternary sequences of period \(N=2np\) with three-level autocorrelation values are constructed, where \(n\) is an arbitrary positive integer and \(\gcd(2n, p)=1\). In particular, if \(n=1\), the quaternary sequence has optimal autocorrelation values. For a family of binary sequences of period \(p\) with optimal Welch bound, a family of quaternary sequences of period \(2p\) with almost optimal Welch bound is constructed.
MSC:
94A55 | Shift register sequences and sequences over finite alphabets in information and communication theory |
11T71 | Algebraic coding theory; cryptography (number-theoretic aspects) |