Linear codes with few weights over $\mathbb{F}_{p}+u\mathbb{F}_{p}$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917705937846272 |
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| author | Kumar, Pavan Khan, Noor Mohammad |
| author_facet | Kumar, Pavan Khan, Noor Mohammad |
| contents | For any positive integer $m$ and an odd prime $p$; let $\mathbb{F}_{q}+u\mathbb{F}_{q}$, where $q=p^{m}$, be a ring extension of the ring $\mathbb{F}_{p}+u\mathbb{F}_{p}.$
In this paper, we construct linear codes over $\mathbb{F}_{p}+u\mathbb{F}_{p}$ by using trace function defined on $\mathbb{F}_{q}+u\mathbb{F}_{q}$ and determine their Hamming weight distributions by employing symplectic-weight distributions of their Gray images. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18325 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear codes with few weights over $\mathbb{F}_{p}+u\mathbb{F}_{p}$ Kumar, Pavan Khan, Noor Mohammad Information Theory 94B05, 11T71 For any positive integer $m$ and an odd prime $p$; let $\mathbb{F}_{q}+u\mathbb{F}_{q}$, where $q=p^{m}$, be a ring extension of the ring $\mathbb{F}_{p}+u\mathbb{F}_{p}.$ In this paper, we construct linear codes over $\mathbb{F}_{p}+u\mathbb{F}_{p}$ by using trace function defined on $\mathbb{F}_{q}+u\mathbb{F}_{q}$ and determine their Hamming weight distributions by employing symplectic-weight distributions of their Gray images. |
| title | Linear codes with few weights over $\mathbb{F}_{p}+u\mathbb{F}_{p}$ |
| topic | Information Theory 94B05, 11T71 |
| url | https://arxiv.org/abs/2406.18325 |