Optimal Rank-Metric Codes with Rank-Locality from Drinfeld Modules
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917201810817024 |
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| author | Bastioni, Luca Darwish, Mohamed O. Micheli, Giacomo |
| author_facet | Bastioni, Luca Darwish, Mohamed O. Micheli, Giacomo |
| contents | We introduce a new technique to construct rank-metric codes using the arithmetic theory of Drinfeld modules over global fields, and Dirichlet Theorem on polynomial arithmetic progressions. Using our methods, we obtain a new infinite family of optimal rank-metric codes with rank-locality, i.e. every code in our family achieves the information theoretical bound for rank-metric codes with rank-locality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06081 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Rank-Metric Codes with Rank-Locality from Drinfeld Modules Bastioni, Luca Darwish, Mohamed O. Micheli, Giacomo Information Theory Number Theory 14G50, 68P30, 11T06 We introduce a new technique to construct rank-metric codes using the arithmetic theory of Drinfeld modules over global fields, and Dirichlet Theorem on polynomial arithmetic progressions. Using our methods, we obtain a new infinite family of optimal rank-metric codes with rank-locality, i.e. every code in our family achieves the information theoretical bound for rank-metric codes with rank-locality. |
| title | Optimal Rank-Metric Codes with Rank-Locality from Drinfeld Modules |
| topic | Information Theory Number Theory 14G50, 68P30, 11T06 |
| url | https://arxiv.org/abs/2407.06081 |