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arXiv · 2606.09448

Explicit and asymptotically good constructions of Algebraic Geometry codes in the sum-rank metric

Peter Beelen·Elena Berardini·Anina Gruica·Maria Montanucci
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Abstract

Algebraic Geometry (AG) codes (i.e. linear codes from algebraic function fields) in the Hamming metric were proposed by Goppa in 1980 and have been intensively studied ever since. Linearized Algebraic Geometry codes, the analogue of AG codes in the sum-rank metric, were instead introduced more recently [9], using quotients of the ring of Ore polynomials with coefficients in an algebraic function field. In this paper, we further investigate the results in [9], providing explicit, optimal and asymptotic constructions.

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Peter Beelen, Elena Berardini, Anina Gruica, Maria Montanucci. 2026-06-08. Explicit and asymptotically good constructions of Algebraic Geometry codes in the sum-rank metric. https://arxiv.org/abs/2606.09448

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