Locally recoverable codes on algebraic curves

Alexander Barg; Itzhak Tamo; Serge Vladut

doi:10.1109/ISIT.2015.7282656

Locally recoverable codes on algebraic curves

Alexander Barg, Itzhak Tamo, Serge Vladut

School of Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Scopus citations

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 (IEEE Trans. Inform. Theory, vol. 60, no. 8, 2014, pp. 4661-4676). 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.

Original language	English
Title of host publication	Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1252-1256
Number of pages	5
ISBN (Electronic)	9781467377041
DOIs	https://doi.org/10.1109/ISIT.2015.7282656
State	Published - 28 Sep 2015
Event	IEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong Duration: 14 Jun 2015 → 19 Jun 2015

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2015-June
ISSN (Print)	2157-8095

Conference

Conference	IEEE International Symposium on Information Theory, ISIT 2015
Country/Territory	Hong Kong
City	Hong Kong
Period	14/06/15 → 19/06/15

Funding

Funders	Funder number
Directorate for Computer and Information Science and Engineering	1217245, 1217894, 1422955
National Sleep Foundation	CCFI217245, CCFI217894, CCFI422955

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10.1109/ISIT.2015.7282656

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Barg, A., Tamo, I., & Vladut, S. (2015). Locally recoverable codes on algebraic curves. In Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015 (pp. 1252-1256). Article 7282656 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2015.7282656

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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 (IEEE Trans. Inform. Theory, vol. 60, no. 8, 2014, pp. 4661-4676). 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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Barg, A, Tamo, I & Vladut, S 2015, Locally recoverable codes on algebraic curves. in Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015., 7282656, IEEE International Symposium on Information Theory - Proceedings, vol. 2015-June, Institute of Electrical and Electronics Engineers Inc., pp. 1252-1256, IEEE International Symposium on Information Theory, ISIT 2015, Hong Kong, Hong Kong, 14/06/15. https://doi.org/10.1109/ISIT.2015.7282656

Locally recoverable codes on algebraic curves. / Barg, Alexander; Tamo, Itzhak; Vladut, Serge.
Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 1252-1256 7282656 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Locally recoverable codes on algebraic curves

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