Trace Representation of Balanced Quaternary Generalized Cyclotomic Sequences of Period pn

Recently, trace representation of a class of balanced quaternary sequences of period p from the classical cyclotomic classes was given by Yang et al. (Cryptogr. Commun.,15 15 (2023): 921-940). In this letter, based on the generalized cyclotomic classes, we define a class of balanced quaternary sequences of period p(n), where p = ef + 1 is an odd prime number and satisfies e equivalent to 0 (mod 4). Furthermore, we calculate the defining polynomial of these sequences and obtain the formula for determining their trace representations over Z(4), by which the linear complexity of these sequences over Z(4) can be determined.