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两类最优循环局部修复码的构造

陈敏, 开晓山   

  1. 合肥工业大学数学学院, 合肥 230601
  • 收稿日期:2021-05-20 修回日期:2021-09-24 出版日期:2022-02-25 发布日期:2022-03-21
  • 基金资助:
    国家自然科学基金(61972126,61772168,61802102)资助课题.

陈敏, 开晓山. 两类最优循环局部修复码的构造[J]. 系统科学与数学, 2022, 42(2): 487-494.

CHEN Min, KAI Xiaoshan. Constructions of Two Classes of Optimal Cyclic Locally Repairable Codes[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(2): 487-494.

Constructions of Two Classes of Optimal Cyclic Locally Repairable Codes

CHEN Min, KAI Xiaoshan   

  1. School of Mathematics, Hefei University of Technology, Hefei 230601
  • Received:2021-05-20 Revised:2021-09-24 Online:2022-02-25 Published:2022-03-21
局部修复码是一种能修复多个故障节点的纠删码,在分布式存储系统中被广泛使用,构造最优局部修复码是目前分布式存储编码理论研究的热点问题之一.文章利用有限域$\mathbb{F}_{q}$上循环码构造了以下两类具有局部修复性$(r,\delta)$的最优局部修复码:1)$[3(q+1),3(q+1)-3\delta+1,\delta+2]$,其中$q\equiv1(\bmod~6)$,$r+\delta-1=q+1$,$2\leq\delta\leq q-1$是偶数;2)$[3(q-1),3(q-1)-3\delta+2,\delta+1]$,其中$q\equiv7(\bmod~9)$,$r+\delta-1=q-1$,$2\leq\delta\leq\frac{2(q-1)}{3}$是偶数且$\delta\not\equiv0(\bmod~6)$.
Locally repairable codes are a class of erasure codes which can repair multiple failed nodes. They are widely used in the distributed storage systems. A main topic in the distributed storage coding is to construct optimal locally repairable codes at present. In this paper, the following two classes of optimal ${(r,\delta)}$ locally repairable codes based on cyclic codes over $\mathbb{F}_{q}$ are constructed:1) $[3(q+1),3(q+1)-3\delta+1,\delta+2]$, where $q\equiv1(\bmod~6)$, $r+\delta-1=q+1$ and $2\leq\delta\leq q-1$ is even; 2) $[3(q-1),3(q-1)-3\delta+2,\delta+1]$, where $q\equiv7(\bmod~9)$, $r+\delta-1=q-1$, $2\leq\delta\leq\frac{2(q-1)}{3}$ is even with $\delta\not\equiv0(\bmod~6)$.

MR(2010)主题分类: 

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