Optimal linear codes with few weights from simplicial complexes
<|reference_start|>Optimal linear codes with few weights from simplicial complexes: Recently, constructions of optimal linear codes from simplicial complexes have attracted much attention and some related nice works were presented. Let $q$ be a prime power. In this paper, by using the simplicial complexes of ${\mathbb F}_{q}^m$ with one single maximal element, we construct four families of linear codes over the ring ${\mathbb F}_{q}+u{\mathbb F}_{q}$ ($u^2=0$), which generalizes the results of [IEEE Trans. Inf. Theory 66(6):3657-3663, 2020]. The parameters and Lee weight distributions of these four families of codes are completely determined. Most notably, via the Gray map, we obtain several classes of optimal linear codes over ${\mathbb F}_{q}$, including (near) Griesmer codes and distance-optimal codes.<|reference_end|>
@article{chen2024optimal,
    title={Optimal linear codes with few weights from simplicial complexes},
    author={Bing Chen, Yunge Xu, Zhao Hu, Nian Li, Xiangyong Zeng},
    journal={arXiv preprint arXiv:2407.10074},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.10074},
    primaryClass={cs.IT math.IT}
}