Linear locally recoverable codes with locality r=1
A code is called a locally recoverable code (LRC) with locality r if any symbol of a codeword can be recovered by accessing r other symbols that forms the recovering set. A LRC has availability t if each symbol has at least t disjoint recovering sets. In this thesis, we summarise the known propertie...
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| 格式: | Theses and Dissertations |
| 語言: | English |
| 出版: |
2017
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| 在線閱讀: | http://hdl.handle.net/10356/69622 |
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| 機構: | Nanyang Technological University |
| 語言: | English |
| 總結: | A code is called a locally recoverable code (LRC) with locality r if any symbol of a codeword can be recovered by accessing r other symbols that forms the recovering set. A LRC has availability t if each symbol has at least t disjoint recovering sets. In this thesis, we summarise the known properties and bounds of linear LRCs and will focus primarily on linear LRCs with locality r = 1 and availability t = 1. We will derive a few propagation rules for linear LRCs with locality r = 1 and present a code construction method using partitions of length n of a LRC. We will prove the optimality of linear LRCs with locality r = 1 for certain values of length n and distance d, and compare upper bounds and lower bounds of binary linear LRCs with locality r = 1 with respect to dimension k. The investigation into the optimal dimensions of linear LRCs is important to improve efficiency in their applications in distributed and cloud storage systems. |
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