Binary $[n,(n\pm1)/2]$ cyclic codes with good minimum distances from sequences
<|reference_start|>Binary $[n,(n\pm1)/2]$ cyclic codes with good minimum distances from sequences: Recently, binary cyclic codes with parameters $[n,(n\pm1)/2,\geq \sqrt{n}]$ have been a hot topic since their minimum distances have a square-root bound. In this paper, we construct four classes of binary cyclic codes $\mathcal{C}_{\mathcal{S},0}$, $\mathcal{C}_{\mathcal{S},1}$ and $\mathcal{C}_{\mathcal{D},0}$, $\mathcal{C}_{\mathcal{D},1}$ by using two families of sequences, and obtain some codes with parameters $[n,(n\pm1)/2,\geq \sqrt{n}]$. For $m\equiv2\pmod4$, the code $\mathcal{C}_{\mathcal{S},0}$ has parameters $[2^m-1,2^{m-1},\geq2^{\frac{m}{2}}+2]$, and the code $\mathcal{C}_{\mathcal{D},0}$ has parameters $[2^m-1,2^{m-1},\geq2^{\frac{m}{2}}+2]$ if $h=1$ and $[2^m-1,2^{m-1},\geq2^{\frac{m}{2}}]$ if $h=2$.<|reference_end|>
@article{xie2024binary,
    title={Binary $[n,(n\pm1)/2]$ cyclic codes with good minimum distances from
  sequences},
    author={Xianhong Xie, Yaxin Zhao, Zhonghua Sun, Xiaobo Zhou},
    journal={arXiv preprint arXiv:2408.01906},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.01906},
    primaryClass={cs.IT math.IT}
}