EAQEC codes from polycyclic codes over the ring $R_l$
DOI:
https://doi.org/10.13069/jacodesmath.v13i2.390Keywords:
Semi-simple ring, Polycyclic codes, Hamming distances, Gray maps, Annihilator dual codesAbstract
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
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