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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.02586 |
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| _version_ | 1866915480792465408 |
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| author | Alnajjarine, Nour Lavrauw, Michel |
| author_facet | Alnajjarine, Nour Lavrauw, Michel |
| contents | An $\mathbb{F}_q$-linear code of minimum distance $d$ is called complete if it is not contained in a larger $\mathbb{F}_q$-linear code of minimum distance $d$. In this paper, we classify $\mathbb{F}_q$-linear complete symmetric rank-distance (CSRD) codes in $M_{3\times 3}(\mathbb{F}_q)$ up to equivalence. This includes the classification of $\mathbb{F}_q$-linear maximum symmetric rank-distance (MSRD) codes in $M_{3\times 3}(\mathbb{F}_q)$. Our approach is mainly geometric, and our results contribute towards the classification of nets of conics in $\mathrm{PG}(2, q)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02586 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear complete symmetric rank-distance codes Alnajjarine, Nour Lavrauw, Michel Combinatorics Algebraic Geometry An $\mathbb{F}_q$-linear code of minimum distance $d$ is called complete if it is not contained in a larger $\mathbb{F}_q$-linear code of minimum distance $d$. In this paper, we classify $\mathbb{F}_q$-linear complete symmetric rank-distance (CSRD) codes in $M_{3\times 3}(\mathbb{F}_q)$ up to equivalence. This includes the classification of $\mathbb{F}_q$-linear maximum symmetric rank-distance (MSRD) codes in $M_{3\times 3}(\mathbb{F}_q)$. Our approach is mainly geometric, and our results contribute towards the classification of nets of conics in $\mathrm{PG}(2, q)$. |
| title | Linear complete symmetric rank-distance codes |
| topic | Combinatorics Algebraic Geometry |
| url | https://arxiv.org/abs/2503.02586 |