Abstract:We construct Locally Recoverable Codes (LRCs) with availability $2$ from a family of fibered surfaces. To obtain the locality and availability properties, and to estimate the minimum distance of the codes, we combine techniques coming from the theory of one-variable function fields and from the theory of fibrations on surfaces. When the locality parameter is $r=3$, we obtain a sharp bound on the minimum distance of the codes. In that case, we give a geometric interpretation of our codes in terms of doubly elliptic surfaces. In particular, this provides the first instance of an error correcting code constructed using a (doubly elliptic) K3 surface.
From: Lara Vicino [view email]
[v1]
Mon, 8 Dec 2025 23:18:08 UTC (43 KB)
[v2]
Sun, 19 Jul 2026 16:52:52 UTC (44 KB)
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