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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2502.18069 |
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| _version_ | 1866910843838398464 |
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| author | Alshuhail, Altaf Betty, Rowena Alma Galvez, Lucky |
| author_facet | Alshuhail, Altaf Betty, Rowena Alma Galvez, Lucky |
| contents | We present some basic theory on the duality of codes over two non-unital rings of order $6$, namely $H_{23}$ and $H_{32}$. For a code $\mathcal{C}$ over these rings, we associate a binary code $\mathcal{C}_a$ and a ternary code $\mathcal{C}_b$. We characterize self-orthogonal, self-dual and quasi self-dual (QSD) codes over these rings using the codes $\mathcal{C}_a$ and $\mathcal{C}_b$. In addition, we present a building-up construction for self-orthogonal codes, introduce cyclic codes and linear complementary dual (LCD) codes. We also gave a classification of self-orthogonal codes for short lengths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18069 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Duality of Codes over Non-unital Rings of Order Six Alshuhail, Altaf Betty, Rowena Alma Galvez, Lucky Information Theory 94B05, 16D10 We present some basic theory on the duality of codes over two non-unital rings of order $6$, namely $H_{23}$ and $H_{32}$. For a code $\mathcal{C}$ over these rings, we associate a binary code $\mathcal{C}_a$ and a ternary code $\mathcal{C}_b$. We characterize self-orthogonal, self-dual and quasi self-dual (QSD) codes over these rings using the codes $\mathcal{C}_a$ and $\mathcal{C}_b$. In addition, we present a building-up construction for self-orthogonal codes, introduce cyclic codes and linear complementary dual (LCD) codes. We also gave a classification of self-orthogonal codes for short lengths. |
| title | Duality of Codes over Non-unital Rings of Order Six |
| topic | Information Theory 94B05, 16D10 |
| url | https://arxiv.org/abs/2502.18069 |