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Sudan, Madhu
The robustness of the tensor product ★★★
Author(s): Ben-Sasson; Sudan
Problem Given two codes
, their Tensor Product
is the code that consists of the matrices whose rows are codewords of
and whose columns are codewords of
. The product
is said to be robust if whenever a matrix
is far from
, the rows (columns) of
are far from
(
, respectively).
![$ R,C $](/files/tex/64f99109c43fb685bfacdfd2575474102a5bf19d.png)
![$ R \otimes C $](/files/tex/d44a6691ed8adef799f58a06521120d25c31d151.png)
![$ R $](/files/tex/201b5ff8bf9045c34a583adc2741b00adf1fd14c.png)
![$ C $](/files/tex/05d3558ef52267cc1af40e658352d98883668ee3.png)
![$ R \otimes C $](/files/tex/d44a6691ed8adef799f58a06521120d25c31d151.png)
![$ M $](/files/tex/3f02401f624e31ef8679d3c3628c1f310058f388.png)
![$ R \otimes C $](/files/tex/d44a6691ed8adef799f58a06521120d25c31d151.png)
![$ M $](/files/tex/3f02401f624e31ef8679d3c3628c1f310058f388.png)
![$ R $](/files/tex/201b5ff8bf9045c34a583adc2741b00adf1fd14c.png)
![$ C $](/files/tex/05d3558ef52267cc1af40e658352d98883668ee3.png)
The problem is to give a characterization of the pairs whose tensor product is robust.
Keywords: codes; coding; locally testable; robustness
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