Locally recoverable codes on algebraic curves

Abstract : A code over a finite alphabet is called locally recoverable (LRC code) if every symbol in the encoding is a function of a small number (at most r) other symbols. A family of linear LRC codes that generalize the classic construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A. Barg. In this paper we extend this construction to codes on algebraic curves. We give a general construction of LRC codes on curves and compute some examples, including asymptotically good families of codes derived from the Garcia- Stichtenoth towers. The local recovery procedure is performed by polynomial interpolation over r coordinates of the codevector. We also obtain a family of Hermitian codes with two disjoint recovering sets for every symbol of the codeword.
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https://hal.archives-ouvertes.fr/hal-01220138
Contributor : Serge Vladuts <>
Submitted on : Saturday, October 24, 2015 - 10:54:51 PM
Last modification on : Monday, March 4, 2019 - 2:04:19 PM

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Barg Alexander, Tamo Itzhak, Vladut Serge, Serge Vladuts. Locally recoverable codes on algebraic curves. . IEEE Int. Sympos. Inform. Theory. 2015, IEEE Inform. Theory Soc., Jun 2015, Hong Kong, Hong Kong SAR China. pp.1252-1256. ⟨hal-01220138⟩

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