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Preprints, Working Papers, ... Year : 2023

Algebraic Geometry codes in the sum-rank metric

Abstract

We introduce the first geometric construction of codes in the sum-rank metric, which we called linearized Algebraic Geometry codes, using quotients of the ring of Ore polynomials with coefficients in the function field of an algebraic curve. We study the parameters of these codes and give lower bounds for their dimension and minimum distance. Our codes exhibit quite good parameters, respecting a similar bound to Goppa's bound for Algebraic Geometry codes in the Hamming metric.
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Dates and versions

hal-04034810 , version 1 (17-03-2023)

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Elena Berardini, Xavier Caruso. Algebraic Geometry codes in the sum-rank metric. 2023. ⟨hal-04034810⟩
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