Rank metric codes from Drinfeld modules
By: Giacomo Micheli, Mihran Papikian
Potential Business Impact:
Builds better codes for computers using math.
We establish a connection between Drinfeld modules and rank metric codes, focusing on the case of semifield codes. Our framework constructs rank metric codes from linear subspaces of endomorphisms of a Drinfeld module, using tools such as characteristic polynomials on Tate modules and the Chebotarev density theorem. We show that Sheekey's construction [She20] fits naturally into this setting, 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.
Similar Papers
Skew polynomial representations of matrix algebras and applications to coding theory
Information Theory
Creates better ways to store and send information.
Decoding rank metric Reed-Muller codes
Information Theory
Unlocks secret codes to fix errors in messages.
Constructions and List Decoding of Sum-Rank Metric Codes Based on Orthogonal Spaces over Finite Fields
Information Theory
Makes data storage more reliable and error-proof.