Bounds and Constructions of Locally Repairable Codes: Parity-check Matrix Approach

@article{Hao2016BoundsAC,
  title={Bounds and Constructions of Locally Repairable Codes: Parity-check Matrix Approach},
  author={Jie Hao and Shu-Tao Xia},
  journal={CoRR},
  year={2016},
  volume={abs/1601.05595}
}
A code symbol of a linear code is said to have locality r if this symbol could be recovered by at most r other code symbols. An (n, k, r) locally repairable code (LRC) with all symbol locality is a linear code with length n, dimension k, and locality r for all symbols. Recently, there are lots of studies on the bounds and constructions of LRCs, most of which are essentially based on the generator matrix of the linear code. Up to now, the most important bounds of minimum distance for LRCs might… CONTINUE READING
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