Cyclic LRC codes and their subfield subcodes

Itzhak Tamo; Alexander Barg; Sreechakra Goparaju; Robert Calderbank

doi:10.1109/ISIT.2015.7282658

Cyclic LRC codes and their subfield subcodes

Itzhak Tamo
, Alexander Barg
, Sreechakra Goparaju
, Robert Calderbank

School of Electrical Engineering

University of Maryland, College Park
University of California at San Diego
Duke University

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

72 Scopus citations

Abstract

We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A. Barg (IEEE Trans. IT, no. 8, 2014). In this paper we focus on the optimal cyclic codes that arise from the general construction. We give a characterization of these codes in terms of their zeros, and observe that there are many equivalent ways of constructing optimal cyclic LRC codes over a given field. We also study subfield subcodes of cyclic LRC codes (BCH-like LRC codes) and establish several results about their locality and minimum distance.

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	1262-1266
Number of pages	5
ISBN (Electronic)	9781467377041
DOIs	https://doi.org/10.1109/ISIT.2015.7282658
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
National Science Foundation	1422955

Access to Document

10.1109/ISIT.2015.7282658

Cite this

Tamo, I., Barg, A., Goparaju, S., & Calderbank, R. (2015). Cyclic LRC codes and their subfield subcodes. In Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015 (pp. 1262-1266). Article 7282658 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2015.7282658

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title = "Cyclic LRC codes and their subfield subcodes",

abstract = "We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A. Barg (IEEE Trans. IT, no. 8, 2014). In this paper we focus on the optimal cyclic codes that arise from the general construction. We give a characterization of these codes in terms of their zeros, and observe that there are many equivalent ways of constructing optimal cyclic LRC codes over a given field. We also study subfield subcodes of cyclic LRC codes (BCH-like LRC codes) and establish several results about their locality and minimum distance.",

author = "Itzhak Tamo and Alexander Barg and Sreechakra Goparaju and Robert Calderbank",

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Tamo, I, Barg, A, Goparaju, S & Calderbank, R 2015, Cyclic LRC codes and their subfield subcodes. in Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015., 7282658, IEEE International Symposium on Information Theory - Proceedings, vol. 2015-June, Institute of Electrical and Electronics Engineers Inc., pp. 1262-1266, IEEE International Symposium on Information Theory, ISIT 2015, Hong Kong, Hong Kong, 14/06/15. https://doi.org/10.1109/ISIT.2015.7282658

Cyclic LRC codes and their subfield subcodes. / Tamo, Itzhak; Barg, Alexander; Goparaju, Sreechakra et al.
Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 1262-1266 7282658 (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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N2 - We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A. Barg (IEEE Trans. IT, no. 8, 2014). In this paper we focus on the optimal cyclic codes that arise from the general construction. We give a characterization of these codes in terms of their zeros, and observe that there are many equivalent ways of constructing optimal cyclic LRC codes over a given field. We also study subfield subcodes of cyclic LRC codes (BCH-like LRC codes) and establish several results about their locality and minimum distance.

AB - We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A. Barg (IEEE Trans. IT, no. 8, 2014). In this paper we focus on the optimal cyclic codes that arise from the general construction. We give a characterization of these codes in terms of their zeros, and observe that there are many equivalent ways of constructing optimal cyclic LRC codes over a given field. We also study subfield subcodes of cyclic LRC codes (BCH-like LRC codes) and establish several results about their locality and minimum distance.

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Cyclic LRC codes and their subfield subcodes

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