Linear complexity and trace representation of Ding–Helleseth generalized cyclotomic quaternary sequences with period pq

In this paper, a generic construction of quaternary sequences is presented by using Ding–Helleseth generalized cyclotomic classes of order d with respect to p q , where p and q are two distinct odd primes with gcd ( p − 1 , q − 1 ) = d . By calculating the discrete Fourier transform of some classical cyclotomic binary sequences derived from this construction, we establish explicit formulas over Z 4 for both the linear complexity and trace representation of the constructed quaternary sequences. As concrete applications, we derive the exact linear complexity and trace representation over Z 4 for two new families of balanced quaternary sequences constructed via Ding–Helleseth generalized cyclotomic classes of order 4 and 8, respectively.