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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2407.04193 |
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| _version_ | 1866912112746430464 |
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| author | Guan, Chaofeng Lv, Jingjie Luo, Gaojun Ma, Zhi |
| author_facet | Guan, Chaofeng Lv, Jingjie Luo, Gaojun Ma, Zhi |
| contents | This paper aims to construct optimal quaternary additive codes with non-integer dimensions. Firstly, we propose combinatorial constructions of quaternary additive constant-weight codes, alongside additive generalized anticode construction. Subsequently, we propose generalized Construction X, which facilitates the construction of non-integer dimensional optimal additive codes from linear codes. Then, we construct ten classes of optimal quaternary non-integer dimensional additive codes through these two methods. As an application, we also determine the optimal additive $[n,3.5,n-t]_4$ codes for all $t$ with variable $n$, except for $t=6,7,12$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Combinatorial Constructions of Optimal Quaternary Additive Codes Guan, Chaofeng Lv, Jingjie Luo, Gaojun Ma, Zhi Information Theory This paper aims to construct optimal quaternary additive codes with non-integer dimensions. Firstly, we propose combinatorial constructions of quaternary additive constant-weight codes, alongside additive generalized anticode construction. Subsequently, we propose generalized Construction X, which facilitates the construction of non-integer dimensional optimal additive codes from linear codes. Then, we construct ten classes of optimal quaternary non-integer dimensional additive codes through these two methods. As an application, we also determine the optimal additive $[n,3.5,n-t]_4$ codes for all $t$ with variable $n$, except for $t=6,7,12$. |
| title | Combinatorial Constructions of Optimal Quaternary Additive Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2407.04193 |