Cyclic LRC codes and their subfield subcodes
Cyclic LRC codes and their subfield subcodes
复制标题
DOI：
10.1109/isit.2015.7282658
复制
发表时间：
2015-02
期刊：
影响因子：
--
通讯作者：
Itzhak Tamo;A. Barg;S. Goparaju;Robert Calderbank
中科院分区：
文献类型：
--
作者：
Itzhak Tamo;A. Barg;S. Goparaju;Robert Calderbank
我们考虑具有局部性属性的线性循环码，或局部可恢复码（LRC 码）。 I. Tamo 和 A. Barg 在最近的一篇论文（IEEE Trans. IT，第 8 期，2014 年）中构建了一系列 LRC 码，它概括了 Reed-Solomon 码的经典构造。在本文中，我们重点关注一般结构中产生的最优循环码。我们根据这些代码的零来描述这些代码的特征，并观察到有许多等效的方法可以在给定字段上构造最佳循环 LRC 代码。我们还研究了循环 LRC 码（类 BCH LRC 码）的子字段子码，并建立了有关其局部性和最小距离的几个结果。
We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A. Barg (IEEE Trans. IT, no. 8, 2014). In this paper we focus on the optimal cyclic codes that arise from the general construction. We give a characterization of these codes in terms of their zeros, and observe that there are many equivalent ways of constructing optimal cyclic LRC codes over a given field. We also study subfield subcodes of cyclic LRC codes (BCH-like LRC codes) and establish several results about their locality and minimum distance.