Constructions of Locally Repairable Codes With Multiple Recovering Sets via Rational Function Fields

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Constructions of Locally Repairable Codes With Multiple Recovering Sets via Rational Function Fields

机译：通过有理函数域构造具有多个恢复集的局部可修复代码

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Locally repairable codes with more than one recovering set are demanded in the application to distributed storage. For each failure node (or disk), it is desired to have as many recovering sets as possible. In this paper, we make use of automorphisms of rational function fields to construct locally repairable codes with multiple recovering sets. Although we focus on two recovering sets, our construction can be easily generalized to the case of multiple recovering sets. In particular, we obtain a class of locally repairable codes with minimum distance only 1 less than the upper bound.

机译：在分布式存储的应用程序中，需要具有多个恢复集的本地可修复代码。对于每个故障节点（或磁盘），希望有尽可能多的恢复集。在本文中，我们利用有理函数域的自同构来构造具有多个恢复集的局部可修复代码。尽管我们专注于两个恢复集，但是我们的构造可以很容易地推广到多个恢复集的情况。特别是，我们获得了一类本地可修复代码，其最小距离仅比上限小1。

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《IEEE Transactions on Information Theory》 |2020年第1期|202-209|共8页
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Fudan Univ Shanghai Key Lab Intelligent Informat Proc Sch Comp Sci Shanghai 200433 Peoples R China|Fudan Univ Shanghai Engn Res Ctr Blockchain Fudan Zhongan Joint Lab Blockchain & Informat Sec Shanghai 200433 Peoples R China|Fudan Univ Shanghai Inst Intelligent Elect & Syst Shanghai 200433 Peoples R China;

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正文语种 eng
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Upper bound; Maintenance engineering; Cost accounting; Indexes; Distributed databases; Blockchain; Education; Locally repairable codes; rational function field; automorphism group;

机译：上限;维修工程;成本会计;索引;分布式数据库;区块链教育;本地可修复代码;有理函数域自同构群;

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1. Construction of Optimal Locally Repairable Codes via Automorphism Groups of Rational Function Fields [J] . IEEE Transactions on Information Theory . 2020,第1期

机译：通过有理函数域的自同构群构造最优的局部可修复代码
2. Construction of Asymptotically Good Locally Repairable Codes via Automorphism Groups of Function Fields [J] . Li Xudong, Ma Liming, Xing Chaoping IEEE Transactions on Information Theory . 2019,第11期

机译：通过功能域的自同构群构造渐近良好的局部可修复码
3. Constructions of Optimal Binary Locally Repairable Codes With Multiple Repair Groups [J] . Jie Hao, Shu-Tao Xia IEEE communications letters . 2016,第6期

机译：具有多个修复组的最佳二进制局部可修复代码的构造
4. Bounds on locally recoverable codes with multiple recovering sets [C] . Tamo, Itzhak, Barg, Alexander Institute of Electrical and Electronics Engineers International Symposium on Information Theory . 2014

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5. Locally Recoverable Codes From Algebraic Curves [D] . Ballentine, Sean. 2018

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7. Construction of Optimal Locally Repairable Codes via Automorphism Groups of Rational Function Fields [O] . Lingfei Jin, Liming Ma, Chaoping Xing 2020

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8. Injectable Sources of Locally Controlled Electrical Fields to Facilitate Tissue Repair. [R] . Kaplan, H. M., Loeb, G. E. 2001

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Constructions of Locally Repairable Codes With Multiple Recovering Sets via Rational Function Fields

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