Infinite families of optimal and minimal codes over rings using simplicial complexes
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929419766988800 |
|---|---|
| author | Wu, Yanan Pang, Tingting Li, Nian Pan, Yanbin Zeng, Xiangyong |
| author_facet | Wu, Yanan Pang, Tingting Li, Nian Pan, Yanbin Zeng, Xiangyong |
| contents | In this paper, several infinite families of codes over the extension of non-unital non-commutative rings are constructed utilizing general simplicial complexes. Thanks to the special structure of the defining sets, the principal parameters of these codes are characterized. Specially, when the employed simplicial complexes are generated by a single maximal element, we determine their Lee weight distributions completely. Furthermore, by considering the Gray image codes and the corresponding subfield-like codes, numerous of linear codes over $\mathbb{F}_q$ are also obtained, where $q$ is a prime power. Certain conditions are given to ensure the above linear codes are (Hermitian) self-orthogonal in the case of $q=2,3,4$. It is noteworthy that most of the derived codes over $\mathbb{F}_q$ satisfy the Ashikhmin-Barg's condition for minimality. Besides, we obtain two infinite families of distance-optimal codes over $\mathbb{F}_q$ with respect to the Griesmer bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09783 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinite families of optimal and minimal codes over rings using simplicial complexes Wu, Yanan Pang, Tingting Li, Nian Pan, Yanbin Zeng, Xiangyong Information Theory In this paper, several infinite families of codes over the extension of non-unital non-commutative rings are constructed utilizing general simplicial complexes. Thanks to the special structure of the defining sets, the principal parameters of these codes are characterized. Specially, when the employed simplicial complexes are generated by a single maximal element, we determine their Lee weight distributions completely. Furthermore, by considering the Gray image codes and the corresponding subfield-like codes, numerous of linear codes over $\mathbb{F}_q$ are also obtained, where $q$ is a prime power. Certain conditions are given to ensure the above linear codes are (Hermitian) self-orthogonal in the case of $q=2,3,4$. It is noteworthy that most of the derived codes over $\mathbb{F}_q$ satisfy the Ashikhmin-Barg's condition for minimality. Besides, we obtain two infinite families of distance-optimal codes over $\mathbb{F}_q$ with respect to the Griesmer bound. |
| title | Infinite families of optimal and minimal codes over rings using simplicial complexes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2407.09783 |