A stabilization theorem for morphism dimensions of supersingular Drinfeld modules yields semifield rank-metric codes.
Rank metric codes from Drinfeld modules
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abstract
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.
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math.NT 1years
2026 1verdicts
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Supersingular Drinfeld modules, Brandt matrices, and rank-metric codes
A stabilization theorem for morphism dimensions of supersingular Drinfeld modules yields semifield rank-metric codes.