EAQEC codes from polycyclic codes over the ring $R_l$

Source abstract

In this paper, we study polycyclic codes over the ring $R_l = \frac{\mathbb{F}_q[w]}{\langle w^l - 1 \rangle}$ with $q = p^k$ where $k$ is a positive integer and $p$ is an odd prime. We explore LCD annihilator, self-dual, self-orthogonal codes over $R_l$ and polycyclic codes over $R_l$. Moreover, we provide a structure of entanglement-assisted quantum error-correcting codes based on the developed polycyclic codes through the inclusion of dual contained conditions. Subsequently, some LCD hull code-derived entanglement-assisted quantum error-correcting code examples are presented.Accepted: 16 March 2026