Salgado CVarilly-Alvarado AVoloch, Jose2021-10-312021-10-312021Salgado C, Varilly-Alvarado A, Voloch JF (2021). Locally recoverable codes on surfaces. IEEE Transactions on Information Theory. abs/1910.13472(9). 5765-5777.0018-94481557-9654https://hdl.handle.net/10092/102797A linear error correcting code is a subspace of a finite-dimensional space over a finite field with a fixed coordinate system. Such a code is said to be locally recoverable with locality r if, for every coordinate, its value at a codeword can be deduced from the value of (certain) r other coordinates of the codeword. These codes have found many recent applications, e.g., to distributed cloud storage. We will discuss the problem of constructing good locally recoverable codes and present some constructions using algebraic surfaces that improve previous constructions and sometimes provide codes that are optimal in a precise sense. The main conceptual contribution of this paper is to consider surfaces fibered over a curve in such a way that each recovery set is constructed from points in a single fiber. This allows us to use the geometry of the fiber to guarantee the local recoverability and use the global geometry of the surface to get a hold on the standard parameters of our codes. We look in detail at situations where the fibers are rational or elliptic curves and provide many examples applying our methods.enAll rights reserved unless otherwise statedcs.ITmath.AGmath.ITJournal Article2021-08-310801 Artificial Intelligence and Image Processing0906 Electrical and Electronic Engineering1005 Communications TechnologiesFields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490401 - Algebra and number theoryFields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490402 - Algebraic and differential geometryFields of Research::40 - Engineering::4006 - Communications engineering::400605 - Optical fibre communication systems and technologiesFields of Research::46 - Information and computing sciences::4606 - Distributed computing and systems software::460604 - Dependable systemshttp://doi.org/10.1109/TIT.2021.3090939