Whitney Numbers of Rank-Metric Lattices and Code Enumeration
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910751456755712 |
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| author | Cotardo, Giuseppe Ravagnani, Alberto Zullo, Ferdinando |
| author_facet | Cotardo, Giuseppe Ravagnani, Alberto Zullo, Ferdinando |
| contents | We investigate the Whitney numbers of the first kind of rank-metric lattices, which are closely linked to the open problem of enumerating rank-metric codes having prescribed parameters. We apply methods from the theory of hyperovals and linear sets to compute these Whitney numbers for infinite families of rank-metric lattices. As an application of our results, we prove asymptotic estimates on the density function of certain rank-metric codes that have been conjectured in previous work. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_13906 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Whitney Numbers of Rank-Metric Lattices and Code Enumeration Cotardo, Giuseppe Ravagnani, Alberto Zullo, Ferdinando Combinatorics Information Theory We investigate the Whitney numbers of the first kind of rank-metric lattices, which are closely linked to the open problem of enumerating rank-metric codes having prescribed parameters. We apply methods from the theory of hyperovals and linear sets to compute these Whitney numbers for infinite families of rank-metric lattices. As an application of our results, we prove asymptotic estimates on the density function of certain rank-metric codes that have been conjectured in previous work. |
| title | Whitney Numbers of Rank-Metric Lattices and Code Enumeration |
| topic | Combinatorics Information Theory |
| url | https://arxiv.org/abs/2412.13906 |