Given two codes R,C, their tensor product $R \otimes C$ consists of all matrices whose rows are codewords of R and whose columns are codewords of C. The product $R \otimes C$ is said to be robust if for every matrix M that is far from $R \otimes C$ it ... more >>>

Given linear two codes R,C, their tensor product $R \otimes C$
consists of all matrices whose rows are codewords of R and whose
columns are codewords of C. The product $R \otimes C$ is said to
be robust if for every matrix M that is far from $R \otimes C$
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We show that random sparse binary linear codes are locally testable and locally decodable (under any linear encoding) with constant queries (with probability tending to one). By sparse, we mean that the code should have only polynomially many codewords. Our results are the first to show that local decodability and ... more >>>