Five-Lee-weight linear codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916313185648640 |
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| author | Kumar, Pavan Khan, Noor Mohammad |
| author_facet | Kumar, Pavan Khan, Noor Mohammad |
| contents | In this study, linear codes having their Lee-weight distributions over the semi-local ring $\mathbb{F}_{q}+u\mathbb{F}_{q}$ with $u^{2}=1$ are constructed using the defining set and Gauss sums for an odd prime $q $. Moreover, we derive complete Hamming-weight enumerators for the images of the constructed linear codes under the Gray map. We finally show an application to secret sharing schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18307 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Five-Lee-weight linear codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}$ Kumar, Pavan Khan, Noor Mohammad Information Theory 94B05, 11T71 In this study, linear codes having their Lee-weight distributions over the semi-local ring $\mathbb{F}_{q}+u\mathbb{F}_{q}$ with $u^{2}=1$ are constructed using the defining set and Gauss sums for an odd prime $q $. Moreover, we derive complete Hamming-weight enumerators for the images of the constructed linear codes under the Gray map. We finally show an application to secret sharing schemes. |
| title | Five-Lee-weight linear codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}$ |
| topic | Information Theory 94B05, 11T71 |
| url | https://arxiv.org/abs/2406.18307 |