Ben-Sasson, Eli

The robustness of the tensor product ★★★

Author(s): Ben-Sasson; Sudan

\begin{problem} Given two codes $R,C$, their \textbf{Tensor Product} $R \otimes C$ is the code that consists of the matrices whose rows are codewords of $R$ and whose columns are codewords of $C$. The product $R \otimes C$ is said to be \textbf{robust} if whenever a matrix $M$ is far from $R \otimes C$, the rows (columns) of $M$ are far from $R$ ($C$, respectively).

The problem is to give a characterization of the pairs $R,C$ whose tensor product is robust. \end{problem}

Keywords: codes; coding; locally testable; robustness

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