The paper introduces a new class of linear codes called \((\sigma, \bar{a})\) -polycyclic codes. By examining their algebraic structure, we obtain certain basic properties of these codes. We show that \((\sigma, \bar{a})\) -polycyclic codes generalize some of the well known classes of linear codes. Further, we describe the class of \({\textbf {1}}\) -generator generalized quasi polycyclic codes and present some results about them. Several results are obtained regarding minimum distances. We also construct some LCD and self orthogonal best known linear codes (BKLCs) from \((\sigma, \bar{a})\) -polycyclic codes.
