Abstract
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 [6]): 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 [13] and Coppersmith and Rudra [9] of codes whose tensor product is not robustly testable.
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