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Locality via Partially Lifted Codes

Authors: S. Luna Frank-Fischer, Venkatesan Guruswami, and Mary Wootters

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)


Abstract
In error-correcting codes, locality refers to several different ways of quantifying how easily a small amount of information can be recovered from encoded data. In this work, we study a notion of locality called the s-Disjoint-Repair-Group Property (s-DRGP). This notion can interpolate between two very different settings in coding theory: that of Locally Correctable Codes (LCCs) when s is large - a very strong guarantee - and Locally Recoverable Codes (LRCs) when s is small - a relatively weaker guarantee. This motivates the study of the s-DRGP for intermediate s, which is the focus of our paper. We construct codes in this parameter regime which have a higher rate than previously known codes. Our construction is based on a novel variant of the lifted codes of Guo, Kopparty and Sudan. Beyond the results on the s-DRGP, we hope that our construction is of independent interest, and will find uses elsewhere.

Cite as

S. Luna Frank-Fischer, Venkatesan Guruswami, and Mary Wootters. Locality via Partially Lifted Codes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{frankfischer_et_al:LIPIcs.APPROX-RANDOM.2017.43,
  author =	{Frank-Fischer, S. Luna and Guruswami, Venkatesan and Wootters, Mary},
  title =	{{Locality via Partially Lifted Codes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{43:1--43:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.43},
  URN =		{urn:nbn:de:0030-drops-75922},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.43},
  annote =	{Keywords: Error correcting codes, locality, lifted codes}
}
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