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Tensor Products of Weakly Smooth Codes AreRobust

机译:弱光滑代码的张量积强健

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摘要

We continue the study of robust tensor codes and expand the class of base codes that can be used as a starting point for the construction of locally testable codes via robust two-wise tensor products. In particular, we show that all unique-neighbor expander codes and all locally correctable codes, when tensored with any other good-distance code, are robust and hence can be used to construct locally testable codes. Previous works by [2] required stronger expansion properties to obtain locally testable codes. Our proofs follow by defining the notion of weakly smooth codes that generalize the smooth codes of [2]. We show that weakly smooth codes are sufficient for constructing robust tensor codes. Using the weaker definition, we are able to expand the family of base codes to include the aforementioned ones.
机译:我们将继续研究鲁棒的张量代码,并扩展基本代码的类型,这些代码可以用作通过鲁棒的双向张量积构造局部可测试代码的起点。特别是,我们表明,所有唯一邻域扩展器代码和所有本地可纠正代码在与任何其他良好距离代码一起张量后,都是健壮的,因此可用于构造本地可测试代码。文献[2]的先前工作要求更强的扩展特性,以获取可本地测试的代码。我们的证明遵循定义弱平滑代码的概念,该概念概括了[2]的平滑代码。我们表明,弱平滑代码足以构造鲁棒的张量代码。使用较弱的定义,我们可以扩展基础代码的家族,以包括上述基础代码。

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