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|Title:||Linear locally recoverable codes with locality r=1||Authors:||Teo, Samuel Tien Ho||Keywords:||DRNTU::Engineering::Computer science and engineering::Data::Coding and information theory||Issue Date:||2017||Source:||Teo, S. T. H. (2017). Linear locally recoverable codes with locality r=1. Master's thesis, Nanyang Technological University, Singapore.||Abstract:||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.||URI:||http://hdl.handle.net/10356/69622||Fulltext Permission:||open||Fulltext Availability:||With Fulltext|
|Appears in Collections:||SPMS Theses|
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|Linear Locally Recoverable Codes with Locality r = 1.pdf||1.06 MB||Adobe PDF|
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