Constructions of Optimal Binary Locally Recoverable Codes via a General Construction of Linear Codes
Constructions of Optimal Binary Locally Recoverable Codes via a General Construction of Linear Codes
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通过线性码的一般构造构造最优二进制局部可恢复码
DOI：
10.1109/tcomm.2021.3083320
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发表时间：
2021-05
期刊：
影响因子：
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通讯作者：
Xiwang Cao
中科院分区：
文献类型：
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作者：
Gaojun Luo;Xiwang Cao
本地可恢复代码在分布式存储系统中起着至关重要的作用。许多研究只关注于构造关于Singleton界的最优局部可恢复码。本文的目的是构造满足字母相关界的最优二进制局部可恢复码。利用与集合相关的线性码的一般框架，我们提供了一种构造局部性为2的二进制局部可恢复码的新方法。我们将设计最优二进制局部可恢复码的问题转化为构造一个合适的集合的问题。利用这种新方法提出了几种最优二进制局部可恢复码的构造方法。最后，我们利用Griesmer码构造了局部性为2、局部性参数为$(\Text{r}，\Delta)$的最优二元局部可恢复码。
Locally recoverable codes play a crucial role in distributed storage systems. Many studies have only focused on the constructions of optimal locally recoverable codes with regard to the Singleton bound. The aim of this paper is to construct optimal binary locally recoverable codes meeting the alphabet-dependent bound. Using a general framework for linear codes associated to a set, we provide a new approach to constructing binary locally recoverable codes with locality 2. We turn the problem of designing optimal binary locally recoverable codes into constructing a suitable set. Several constructions of optimal binary locally recoverable codes are proposed by this new method. Finally, we propose constructions of optimal binary locally recoverable codes with locality 2 and locality parameters $(\text {r},\delta)$ by Griesmer codes.