Unequal locality and recovery for Locally Recoverable Codes with availability
Unequal locality and recovery for Locally Recoverable Codes with availability
复制标题
具有可用性的本地可恢复代码的不平等位置和恢复
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Thangaraj
中科院分区：
文献类型：
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作者：
Sourbh Bhadane;A. Thangaraj
如果一个代码的每个坐标都可以从多个不相交的坐标集合（称为恢复集合）中恢复出来，则该代码被称为具有可用性的局部可恢复代码（LRC）。恢复集的大小称为局部性。在这项工作中，我们考虑LRC与两种不同的设置下的可用性不平等的恢复集大小固定的所有坐标或不平等的地方在多个坐标。对于每一个设置，我们推导出的最小距离，推广以前已知的界限的情况下，不平等的恢复和不平等的地方，并证明使用类似的技术。对于平等的恢复和可用性的地方的情况下，我们表明，一个已知的多项式评估建设扩展到最佳的代码在特定的情况下，所有符号的地方。
A code is said to be a Locally Recoverable Code (LRC) with availability if every coordinate can be recovered from multiple disjoint sets of other coordinates called recovering sets. The size of a recovering set is called locality. In this work, we consider LRCs with availability under two different settings-unequal recovery set sizes fixed for all coordinates or unequal locality over multiple coordinates. For each setting, we derive bounds for the minimum distance that generalize previously known bounds to the cases of unequal recovery and unequal locality, and are proved using similar techniques. For the case of equal recovery and locality with availability, we show that a known polynomial-evaluation construction extends to optimal codes with all-symbol locality in a specific case.