Locally Testable Codes and PCPs of Almost-Linear Length
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The tensor product of two codes is not necessarily robustly testable
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Robust local testability of tensor products of LDPC codes
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Composition of Semi-LTCs by Two-Wise Tensor Products
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Guest column: testing linear properties: some general theme
ACM SIGACT News
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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.