New QEC codes and EAQEC codes from repeated-root cyclic codes of length $2^rp^s$
<|reference_start|>New QEC codes and EAQEC codes from repeated-root cyclic codes of length $2^rp^s$: Let $p$ be an odd prime and $r,s,m$ be positive integers. In this study, we initiate our exploration by delving into the intricate structure of all repeated-root cyclic codes and their duals with a length of $2^rp^s$ over the finite field $\mathbb{F}_{p^m}$. Through the utilization of CSS and Steane's constructions, a series of new quantum error-correcting (QEC) codes are constructed with parameters distinct from all previous constructions. Furthermore, we provide all maximum distance separable (MDS) cyclic codes of length $2^rp^s$, which are further utilized in the construction of QEC MDS codes. Finally, we introduce a significant number of novel entanglement-assisted quantum error-correcting (EAQEC) codes derived from these repeated-root cyclic codes. Notably, these newly constructed codes exhibit parameters distinct from those of previously known constructions.<|reference_end|>
@article{li2024new,
    title={New QEC codes and EAQEC codes from repeated-root cyclic codes of length
  $2^rp^s$},
    author={Lanqiang Li, Ziwen Cao, Tingting Wu, Li Liu},
    journal={arXiv preprint arXiv:2406.13943},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.13943},
    primaryClass={cs.IT math.IT}
}