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On binary locally repairable codes with distance four
Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2021-01-07 , DOI: 10.1016/j.ffa.2020.101793
Ruihu Li , Sen Yang , Yi Rao , Qiang Fu

We propose a unified construction for binary locally repairable codes (LRCs) with distance four. When there is a binary linear code [n,k,4] without all zero coordinates, we can construct a binary LRC [n,k,4] with very good locality r. Conditions for which these LRCs attain the Cadambe-Mazumdar bound are also presented. We prove that all our LRCs with locality r3 are optimal LRCs, and most of our LRCs with locality r4 can achieve the Cadambe-Mazumdar bound. Especially, if n256, all the constructed distance optimal [n,k,4] LRCs, except 17 codes, can achieve the Cadambe-Mazumdar bound. We also show that six known constructions are covered in our construction, and eight known constructions can be improved by our construction.



中文翻译:

在距离为4的二进制本地可修复代码上

我们为距离为4的二进制本地可修复代码(LRC)提出了统一的构造。有二进制线性代码时[ñķ4] 没有所有零坐标,我们可以构造一个二进制LRC [ñķ4]有很好的地方r。还介绍了这些LRC达到Cadambe-Mazumdar界限的条件。我们证明我们所有本地的LRC[R3 是最佳的LRC,而我们的大多数LRC都具有局部性 [R4可以达到Cadambe-Mazumdar的界线。特别是如果ñ256,所有构造的距离最佳 [ñķ4]除17个代码外,LRC可以达到Cadambe-Mazumdar边界。我们还表明,我们的结构涵盖了六个已知的构造,并且我们的构造可以改进八个已知的构造。

更新日期:2021-01-07
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