Robust Local Testability of Tensor Products of LDPC Codes
Given two binary linear codes R and C, their tensor product R⊗C consists of all matrices with rows in R and columns in C. We analyze the “robustness” of the following test for this code (suggested by Ben-Sasson and Sudan ): Pick a random row (or column) and check if the received word is in R (or C). Robustness of the test implies that if a matrix M is far from R⊗C, then a significant fraction of the rows (or columns) of M are far from codewords of R (or C).
We show that this test is robust, provided one of the codes is what we refer to as smooth. We show that expander codes and locally-testable codes are smooth. This complements recent examples of P. Valiant  and Coppersmith and Rudra  of codes whose tensor product is not robustly testable.
KeywordsTensor Product Linear Code Parity Check Local View Testable Code
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