**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).

The problem is to give a characterization of the pairs whose tensor product is robust.

The question is studied in the context of Locally Testable Codes.

## Bibliography

*[BS] Eli Ben-Sasson, Madhu Sudan, Robust locally testable codes and products of codes, APPROX-RANDOM 2004, pp. 286-297 (See ECCC TR04-046).

[CR] D. Coppersmith and A. Rudra, On the robust testability of tensor products of codes, ECCC TR07-061.

[DSW] Irit Dinur, Madhu Sudan and Avi Wigderson, Robust local testability of tensor products of LDPC codes, APPROX-RANDOM 2006, pp. 304-315 (See ECCC TR06-118).

[GM] Oded Goldreich, Or Meir, The Tensor Product of Two Good Codes Is Not Necessarily Robustly Testable, ECCC TR07-062.

[M] Or Meir, On the Rectangle Method in proofs of Robustness of Tensor Products, ECCC TR07-061.

[V] Paul Valiant, The Tensor Product of Two Codes Is Not Necessarily Robustly Testable, APPROX-RANDOM 2005, pp. 472-481.

* indicates original appearance(s) of problem.