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2026-01-07 07:04 UTC · math.NT · math.NT, cs.IT, math.CO

Rank metric codes from Drinfeld modules

Giacomo Micheli, Mihran Papikian

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.
arXiv abstractPDF

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