SIAM Journal on Computing, Ahead of Print.
We show that the tensor product of a high-rate globally list recoverable code is (approximately) locally list recoverable. List recovery has been a useful building block in the design of list decodable codes, and our motivation is to use the tensor construction as such a building block. In particular, instantiating this construction with known constructions of high-rate globally list recoverable codes, and using appropriate transformations, we obtain the first capacity-achieving locally list decodable codes (over a large constant size alphabet), and the first capacity-achieving globally list decodable codes with nearly linear time list decoding algorithms. Our techniques are inspired by an approach of Gopalan, Guruswami, and Raghavendra [SIAM J. Comput., 40 (2011), pp. 1432--1462] for list decoding tensor codes.

中文翻译：

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高速张量代码和应用程​​序的本地列表恢复

《 SIAM计算杂志》，预印本。
我们表明，高速率全局列表可恢复代码的张量积是（大约）本地列表可恢复的。列表恢复一直是列表可解码代码设计中的有用构建基块，我们的动机是使用张量构建作为构建基块。特别是，用已知的高速率全局列出可恢复代码的构造实例化此构造，并使用适当的转换，我们获得第一个实现容量的本地列表可解码代码（在较大的恒定大小的字母上），以及第一个实现全局容量的可解码代码使用几乎线性的时间列表解码算法列出可解码代码。我们的技术是受Gopalan，Guruswami和Raghavendra [SIAM J. Comput。，40（2011），pp.1432--1462]的方法进行启发的，该方法用于对张量代码进行列表解码。