Locally Recoverable Codes with Availability t≥2 from Fiber Products of Curves
Locally Recoverable Codes with Availability t≥2 from Fiber Products of Curves
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DOI：
10.3934/amc.2018020
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发表时间：
2016-12
期刊：
影响因子：
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通讯作者：
Kathryn Haymaker;Beth Malmskog;Gretchen L. Matthews
中科院分区：
文献类型：
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作者：
Kathryn Haymaker;Beth Malmskog;Gretchen L. Matthews
我们通过利用曲线的纤维积结构，将巴尔格（Barg）、塔莫（Tamo）和弗勒杜茨（Vlăduţ）给出的代数曲线上局部可恢复码的构造推广到具有任意多个恢复集的情况。利用极大曲线，我们创建了几个具有多个恢复集的新的局部可恢复码族，包括来自广义朱列蒂（Giulietti）和科尔奇马罗斯（Korchmáros）（GK）曲线以及铃木曲线的具有两个恢复集的码，以及基于埃尔米特曲线利用范德吉尔（van der Geer）和范德弗勒格特（van der Vlugt）的纤维积构造的具有许多恢复集的新的局部可恢复码。此外，我们考虑了局部错误恢复和全局错误纠正之间的关系，以及局部恢复固定数量擦除的任何模式所需的可用性。
We generalize the construction of locally recoverable codes on algebraic curves given by Barg, Tamo and Vl\u{a}du\c{t} to those with arbitrarily many recovery sets by exploiting the structure of fiber products of curves. Employing maximal curves, we create several new families of locally recoverable codes with multiple recovery sets, including codes with two recovery sets from the generalized Giulietti and Korchm\'{a}ros (GK) curves and the Suzuki curves, and new locally recoverable codes with many recovery sets based on the Hermitian curve, using a fiber product construction of van der Geer and van der Vlugt. In addition, we consider the relationship between local error recovery and global error correction as well as the availability required to locally recover any pattern of a fixed number of erasures.