Autocorrelation function of a family of complex sequences (Q1335330)

Starting with GMW sequences [IEEE Trans. Inf. Theory 30, 548-553 (1984; Zbl 0544.65005)] over \(GF (2^ k)\), generalized GMW sequences over \(GF (p^ k)\) for \(k= k_ 1 \cdot \dots \cdot k_ t\) are constructed by using trace functions of the field extensions \(GF (p^{k_ 1\cdot \dots\cdot k_ s} )\subseteq GF (p^{k_ 1\cdot \dots\cdot k_{s+1}})\) and a primitive element of \(GF (p^ k)\). It is shown that the complex sequences obtained in this way have optimal autocorrelation properties. Finally, statistical properties are stated and the number of generalized GMW sequences according to the choice of \(p\) and \(k_ 1,\dots, k_ t\) is given.