Rank metric codes from Drinfeld modules
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910121708224512 |
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| author | Micheli, Giacomo Papikian, Mihran |
| author_facet | Micheli, Giacomo Papikian, Mihran |
| contents | We establish a connection between Drinfeld modules and rank-metric codes, focusing on the case of semifield codes. Our method constructs rank-metric codes from linear subspaces of endomorphisms of a Drinfeld module acting on torsion submodules. We show that Sheekey's construction [She20] fits naturally into this framework, yielding a short conceptual proof of one of his main results. We then give a new construction of infinite families of semifield codes arising from Drinfeld modules defined over finite fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03653 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rank metric codes from Drinfeld modules Micheli, Giacomo Papikian, Mihran Number Theory Information Theory Combinatorics 11G09, 12K10, 11T71, 16S36 We establish a connection between Drinfeld modules and rank-metric codes, focusing on the case of semifield codes. Our method constructs rank-metric codes from linear subspaces of endomorphisms of a Drinfeld module acting on torsion submodules. We show that Sheekey's construction [She20] fits naturally into this framework, yielding a short conceptual proof of one of his main results. We then give a new construction of infinite families of semifield codes arising from Drinfeld modules defined over finite fields. |
| title | Rank metric codes from Drinfeld modules |
| topic | Number Theory Information Theory Combinatorics 11G09, 12K10, 11T71, 16S36 |
| url | https://arxiv.org/abs/2601.03653 |