2025/12/08 by Cecília Salgado, Lara Vicino, Salgado, Cecília +1
Computer Science · Mathematics · #Advanced Data Storage Technologies #Coding theory and cryptography #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.2512.08100
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.