Locally recoverable codes on surfaces

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dc.contributor.authorSalgado C
dc.contributor.authorVarilly-Alvarado A
dc.contributor.authorVoloch, Jose
dc.date.accessioned2021-10-31T20:59:10Z
dc.date.available2021-10-31T20:59:10Z
dc.date.issued2021en
dc.date.updated2021-08-31T12:17:59Z
dc.description.abstractA 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.en
dc.identifier.citationSalgado C, Varilly-Alvarado A, Voloch JF (2021). Locally recoverable codes on surfaces. IEEE Transactions on Information Theory. abs/1910.13472(9). 5765-5777.en
dc.identifier.doihttp://doi.org/10.1109/TIT.2021.3090939
dc.identifier.issn0018-9448
dc.identifier.issn1557-9654
dc.identifier.urihttps://hdl.handle.net/10092/102797
dc.language.isoen
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.rightsAll rights reserved unless otherwise stateden
dc.rights.urihttp://hdl.handle.net/10092/17651en
dc.subjectcs.ITen
dc.subjectmath.AGen
dc.subjectmath.ITen
dc.subject.anzsrc0801 Artificial Intelligence and Image Processingen
dc.subject.anzsrc0906 Electrical and Electronic Engineeringen
dc.subject.anzsrc1005 Communications Technologiesen
dc.subject.anzsrcFields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490401 - Algebra and number theoryen
dc.subject.anzsrcFields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490402 - Algebraic and differential geometryen
dc.subject.anzsrcFields of Research::40 - Engineering::4006 - Communications engineering::400605 - Optical fibre communication systems and technologiesen
dc.subject.anzsrcFields of Research::46 - Information and computing sciences::4606 - Distributed computing and systems software::460604 - Dependable systemsen
dc.titleLocally recoverable codes on surfacesen
dc.typeJournal Articleen
uc.collegeFaculty of Engineering
uc.departmentMathematics and Statistics
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