Quantum codes construction from skew polycyclic codes

Abstract

This paper establishes the relation between skew polycyclic and skew sequential codes over a finite field. We prove with different induced vectors that right Θ-polycyclic codes are left Θ−1-polycyclic codes. Further, we characterize the condition under which a code is both left and right skew polycyclic with the same induced vectors. Moreover, an analogous study is also discussed for skew sequential codes. Further, to show the novelty of our work, many examples of "MDS (Maximum Distance Separable)" codes are provided. Finally, as an application, we construct quantum codes with good parameters from these codes.