A generalization of the Hall’s sextic residue sequences

Let p be a prime with 6∣(p − 1) and integer m ⩾ 1. As a generalization of the Hall’s sextic residue sequences, we introduce some families of generalized cyclotomic binary sequences over the residue class ring modulo pm by defining sextic generalized cyclotomic residue classes. We determine the values of the linear complexity, which are large enough to resist security attacks using the Berlekamp–Massey algorithm. We also investigate the trace function representation for the resulting sequences when m = 2.