Generalized integrated interleaved (GII) codes have attracted increasing research interests in distributed storage systems, since they can achieve a good tradeoff between correction capability and locality. A GII code can be characterized by a conversion matrix that satisfies a specific constraint. In the literature, only two- and three-layer GII codes have been proposed, as it is not easy to construct a valid conversion matrix that satisfies the constraint required by the GII codes with more layers. In this letter, we propose a method to construct multi-layer (more than three) GII codes, providing more flexibility on the code construction. Compared with the existing two- and three-layer GII codes, the multi-layer GII codes can achieve better locality.

中文翻译：

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多层广义综合交织码

广义集成交织（GII）码在分布式存储系统中引起了越来越多的研究兴趣，因为它们可以在校正能力和局部性之间实现良好的折衷。GII 代码可以通过满足特定约束的转换矩阵来表征。在文献中，仅提出了两层和三层 GII 代码，因为构建满足更多层 GII 代码所需约束的有效转换矩阵并不容易。在这封信中，我们提出了一种构建多层（三个以上）GII 代码的方法，为代码构建提供了更大的灵活性。与现有的两层和三层GII码相比，多层GII码可以实现更好的局部性。