Tensor Products of Weakly Smooth Codes are Robust
Tensor Products of Weakly Smooth Codes are Robust
复制标题
弱平滑码的张量积是鲁棒的
DOI：
10.4086/toc.2009.v005a012
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
M. Viderman
中科院分区：
文献类型：
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作者：
Eli Ben;M. Viderman
我们继续研究的robusttensor代码和扩展类的基本代码，可以作为一个起点，通过强大的两个明智的张量积的本地可测试的代码的建设。特别是，我们证明了所有唯一邻居扩展码和所有局部可纠正码，当张量与任何其他良好的距离码，是强大的，因此可以用来构造局部可测试码。[2]以前的工作需要更强的扩展性质来获得局部可测码。
我们的证明遵循定义弱smoothcodes的概念，推广smoothcodes的[2]。我们证明了弱光滑码是构造鲁棒张量码的充分条件。使用较弱的定义，我们能够扩展基码族以包括上述基码。
We continue the study of robusttensor 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 smoothcodes that generalize the smoothcodes 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.