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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.737

List Decoding Group Homomorphisms Between Supersolvable Groups

Authors: Alan Guo and Madhu Sudan

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract

We show that the set of homomorphisms between two supersolvable groups can be locally list decoded up to the minimum distance of the code, extending the results of Dinur et al. (Proc. STOC 2008) who studied the case where the groups are abelian. Moreover, when specialized to the abelian case, our proof is more streamlined and gives a better constant in the exponent of the list size. The constant is improved from about 3.5 million to 105.

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Alan Guo and Madhu Sudan. List Decoding Group Homomorphisms Between Supersolvable Groups. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 737-747, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{guo_et_al:LIPIcs.APPROX-RANDOM.2014.737,
  author =	{Guo, Alan and Sudan, Madhu},
  title =	{{List Decoding Group Homomorphisms Between Supersolvable Groups}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{737--747},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.737},
  URN =		{urn:nbn:de:0030-drops-47359},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.737},
  annote =	{Keywords: Group theory, error-correcting codes, locally decodable codes}
}

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List Decoding Group Homomorphisms Between Supersolvable Groups

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