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Designs, Codes and Cryptography

, Volume 86, Issue 2, pp 419–445 | Cite as

Anticode-based locally repairable codes with high availability

  • Natalia Silberstein
  • Alexander Zeh
Article
  • 184 Downloads
Part of the following topical collections:
  1. Special Issue on Network Coding and Designs

Abstract

This paper presents constructions of new families of locally repairable codes (LRCs) with small locality and high availability, where each code symbol can be recovered by using many (exponential in the dimension of the code) disjoint small sets (of size 2 or 3) of other code symbols. Following the method of Farrell, the generator matrices of our LRCs are obtained by deleting certain columns from the generator matrix of the Simplex code, where the deleted columns form different anticodes. Most of the resulting codes, defined over any finite field and in particular over the binary field, are optimal either with respect to the Griesmer bound, or with respect to the Cadambe–Mazumdar bound for LRCs, or both.

Keywords

Anticodes Availability Coding for distributed storage systems Locally repairable codes 

Mathematics Subject Classification

94B60 11T71 

Notes

Acknowledgements

The authors thank the anonymous reviewers for their valuable comments and suggestions that helped to improve the quality of the paper. A. Zeh has been supported by the German research council (Deutsche Forschungsgemeinschaft, DFG) under Grant Ze1016/1-1.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceTechnion—Israel Institute of TechnologyHaifaIsrael
  2. 2.Department of Electrical and Computer EngineeringBen-Gurion University of the NegevBeer ShevaIsrael
  3. 3.Yahoo! LabsHaifaIsrael
  4. 4.Infineon Technologies AGNeubibergGermany

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