Optimal linear codes with few weights from simplicial complexes
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911955053182976 |
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| author | Chen, Bing Xu, Yunge Hu, Zhao Li, Nian Zeng, Xiangyong |
| author_facet | Chen, Bing Xu, Yunge Hu, Zhao Li, Nian Zeng, Xiangyong |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_10074 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal linear codes with few weights from simplicial complexes Chen, Bing Xu, Yunge Hu, Zhao Li, Nian Zeng, Xiangyong Information Theory 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. |
| title | Optimal linear codes with few weights from simplicial complexes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2407.10074 |