Document Open Access Logo

List Decoding Group Homomorphisms Between Supersolvable Groups

Authors Alan Guo, Madhu Sudan

PDF
Thumbnail PDF

File

LIPIcs.APPROX-RANDOM.2014.737.pdf
  • Filesize: 0.53 MB
  • 11 pages

Document Identifiers

Author Details

Alan Guo
Madhu Sudan

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2014.737

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.

Subject Classification

Keywords
  • Group theory
  • error-correcting codes
  • locally decodable codes

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Irit Dinur, Elena Grigorescu, Swastik Kopparty, and Madhu Sudan. Decodability of group homomorphisms beyond the Johnson bound. In Dwork [2], pages 275-284. Google Scholar
  2. Cynthia Dwork, editor. Proceedings of the 40th Annual ACM Symposium on Theory of Computing, Victoria, British Columbia, Canada, May 17-20, 2008. ACM, 2008. Google Scholar
  3. Oded Goldreich and Leonid A. Levin. A hard-core predicate for all one-way functions. In David S. Johnson, editor, STOC, pages 25-32. ACM, 1989. Google Scholar
  4. Parikshit Gopalan. A Fourier-analytic approach to Reed-Muller decoding. IEEE Transactions on Information Theory, 59(11):7747-7760, 2013. Google Scholar
  5. Parikshit Gopalan, Venkatesan Guruswami, and Prasad Raghavendra. List decoding tensor products and interleaved codes. SIAM Journal on Computing, 40(5):1432-1462, 2011. Google Scholar
  6. Parikshit Gopalan, Adam R. Klivans, and David Zuckerman. List-decoding Reed-Muller codes over small fields. In Dwork [2], pages 265-274. Google Scholar
  7. Elena Grigorescu, Swastik Kopparty, and Madhu Sudan. Local decoding and testing for homomorphisms. In Josep Díaz, Klaus Jansen, José D. P. Rolim, and Uri Zwick, editors, APPROX-RANDOM, volume 4110 of Lecture Notes in Computer Science, pages 375-385. Springer, 2006. Google Scholar
  8. Alan Guo. Group homomorphisms as error correcting codes, April 2014. URL: http://arxiv.org/abs/1404.3447.
  9. Venkatesan Guruswami. Linear-algebraic list decoding of folded Reed-Solomon codes. In IEEE Conference on Computational Complexity, pages 77-85. IEEE Computer Society, 2011. Google Scholar
  10. Venkatesan Guruswami and Atri Rudra. Explicit codes achieving list decoding capacity: Error-correction with optimal redundancy. IEEE Transactions on Information Theory, 54(1):135-150, 2008. Google Scholar
  11. Venkatesan Guruswami and Carol Wang. Optimal rate list decoding via derivative codes. In Leslie Ann Goldberg, Klaus Jansen, R. Ravi, and José D. P. Rolim, editors, APPROX-RANDOM, volume 6845 of Lecture Notes in Computer Science, pages 593-604. Springer, 2011. Google Scholar
  12. Swastik Kopparty. List-decoding multiplicity codes. Electronic Colloquium on Computational Complexity (ECCC), 19:44, 2012. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact