Polycyclic codes over serial rings and their annihilator CSS construction
<|reference_start|>Polycyclic codes over serial rings and their annihilator CSS construction: In this paper, we investigate the algebraic structure for polycyclic codes over a specific class of serial rings, defined as $\mathscr R=R[x_1,\ldots, x_s]/\langle t_1(x_1),\ldots, t_s(x_s) \rangle$, where $R$ is a chain ring and each $t_i(x_i)$ in $R[x_i]$ for $i\in\{1,\ldots, s\}$ is a monic square-free polynomial. We define quasi-$s$-dimensional polycyclic codes and establish an $R$-isomorphism between these codes and polycyclic codes over $\mathscr R$. We provide necessary and sufficient conditions for the existence of annihilator self-dual, annihilator self-orthogonal, annihilator linear complementary dual, and annihilator dual-containing polycyclic codes over this class of rings. We also establish the CSS construction for annihilator dual-preserving polycyclic codes over the chain ring $R$ and use this construction to derive quantum codes from polycyclic codes over $\mathscr{R}$.<|reference_end|>
@article{bajalan2024polycyclic,
    title={Polycyclic codes over serial rings and their annihilator CSS
  construction},
    author={Maryam Bajalan, Edgar Martinez-Moro},
    journal={arXiv preprint arXiv:2404.10452},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.10452},
    primaryClass={cs.IT math.IT}
}