The minimum weight of the code of intersecting lines in ${\rm PG}(3,q)$
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908789053063168 |
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| author | Adriaensen, Sam Simoens, Robin Storme, Leo |
| author_facet | Adriaensen, Sam Simoens, Robin Storme, Leo |
| contents | We characterise the minimum weight codewords of the $p$-ary linear code of intersecting lines in ${\rm PG}(3,q)$, $q=p^h$, $q\geq19$, $p$ prime, $h\geq 1$. If $q$ is even, the minimum weight equals $q^3+q^2+q+1$. If $q$ is odd, the minimum weight equals $q^3+2q^2+q+1$. For $q$ even, we also characterise the codewords of second smallest weight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07451 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The minimum weight of the code of intersecting lines in ${\rm PG}(3,q)$ Adriaensen, Sam Simoens, Robin Storme, Leo Combinatorics 05B25, 51A50, 51E21, 94B05 We characterise the minimum weight codewords of the $p$-ary linear code of intersecting lines in ${\rm PG}(3,q)$, $q=p^h$, $q\geq19$, $p$ prime, $h\geq 1$. If $q$ is even, the minimum weight equals $q^3+q^2+q+1$. If $q$ is odd, the minimum weight equals $q^3+2q^2+q+1$. For $q$ even, we also characterise the codewords of second smallest weight. |
| title | The minimum weight of the code of intersecting lines in ${\rm PG}(3,q)$ |
| topic | Combinatorics 05B25, 51A50, 51E21, 94B05 |
| url | https://arxiv.org/abs/2403.07451 |