• TUCS Publication Series
• How to Publish in TUCS Series
• Publication Search
• Publication Graph
• Publication Input
• Publication Input Guide
• JuFo Browser

Constructions of Optimal and Almost Optimal Locally Repairable Codes

Toni Ernvall, Thomas Westerbäck, Camilla Hollanti, Constructions of Optimal and Almost Optimal Locally Repairable Codes. In: 2014 4th International Conference on Wireless Communications, Vehicular Technology, Information Theory and Aerospace & Electronic Systems (VITAE), 1–5, IEEE, 2014.

http://dx.doi.org/10.1109/VITAE.2014.6934442

Abstract:

Constructions of optimal locally repairable codes (LRCs) in the case of (r + 1) ł n and over small finite fields were stated as open problems for LRCs in [I. Tamo et al., “Optimal locally repairable codes and connections to matroid theory”, 2013 IEEE ISIT]. In this paper, these problems are studied by constructing almost optimal linear LRCs, which are proven to be optimal for certain parameters, including cases for which (r + 1) ł n. More precisely, linear codes for given length, dimension, and all-symbol locality are constructed with almost optimal minimum distance. `Almost optimal' refers to the fact that their minimum distance differs by at most one from the optimal value given by a known bound for LRCs. In addition to these linear LRCs, optimal LRCs which do not require a large field are constructed for certain classes of parameters.

BibTeX entry:

@INPROCEEDINGS{inpErWeHo14a,
  title = {Constructions of Optimal and Almost Optimal Locally Repairable Codes},
  booktitle = {2014 4th International Conference on Wireless Communications, Vehicular Technology, Information Theory and Aerospace & Electronic Systems (VITAE)},
  author = {Ernvall, Toni and Westerbäck, Thomas and Hollanti, Camilla},
  publisher = {IEEE},
  pages = {1–5},
  year = {2014},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

Edit publication