Bounds and constructions for linear locally repairable codes over binary fields
Bounds and constructions for linear locally repairable codes over binary fields
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DOI：
10.1109/isit.2017.8006886
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发表时间：
2017-01
期刊：
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通讯作者：
Anyu Wang;Zhifang Zhang;D. Lin
中科院分区：
文献类型：
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作者：
Anyu Wang;Zhifang Zhang;D. Lin
对于二元[n，k，d]线性局部可修码，导出了k的两个新的上界.第一个适用于LRC与不相交的局部修复群，一般值的n，d和局部r，包含一些以前已知的界限作为特殊情况。第二种是基于求解一个优化问题，适用于具有任意局部修复组结构的LRC。特别地，当d ≥ 5时，从第二界导出了一个显式界.一个具体的比较表明，该显式界优于Cadambe-Mazumdar界5 ≤ d ≤ 8和大的值n。此外，还构造了一个达到第二界的d ≥ 6的二元线性LRC.
For binary [n, k, d] linear locally repairable codes (LRCs), two new upper bounds on k are derived. The first one applies to LRCs with disjoint local repair groups, for general values of n, d and locality r, containing some previously known bounds as special cases. The second one is based on solving an optimization problem and applies to LRCs with arbitrary structure of local repair groups. Particularly, an explicit bound is derived from the second bound when d ≥ 5. A specific comparison shows this explicit bound outperforms the Cadambe-Mazumdar bound for 5 ≤ d ≤ 8 and large values of n. Moreover, a construction of binary linear LRCs with d ≥ 6 attaining our second bound is provided.