We define linear codes which are s-Locally Recoverable Codes (or s-LRC), i.e. codes which are LRC in s ways, the case \(s=1\) roughly corresponding to the classical case of LRC codes. We use them to describe codes which correct many erasures, although they have small minimum distance. Any letter of a received word may be corrected using s different local codes. We use the Segre embedding of s local codes and then a linear projection.

中文翻译：

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本地可恢复代码可纠正小范围内的许多擦除

我们定义了s -Locally Recoverable Codes（或s -LRC）的线性码，即以s种方式是LRC的码，情况\(s=1\)大致对应于LRC码的经典情况。我们使用它们来描述可以纠正许多擦除的代码，尽管它们的最小距离很小。一个接收的字中的任何字母可以使用被校正小号不同的本地码。我们使用s 个本地代码的 Segre 嵌入，然后使用线性投影。