The tensor product of two good codes is not necessarily robustly testable

Information Processing Letters

Volumn 112, Issue 8-9, 2012, Pages 351-355

  Goldreich, Oded ^a   Meir, Or ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Locally testable codes; Product code; Robust; Robustness; Tensor product; Theory of computation

Indexed keywords

LOCALLY TESTABLE CODES; PRODUCT CODE; ROBUST; TENSOR PRODUCT; THEORY OF COMPUTATION;

COMPUTATION THEORY; ROBUSTNESS (CONTROL SYSTEMS);

CODES (SYMBOLS);

EID: 84856609326     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ipl.2012.01.007     Document Type: Article

References (18)

1. Eli Ben-Sasson, Oded Goldreich, Prahladh Harsha, Madhu Sudan, and Salil Vadhan Robust PCPs of proximity, shorter PCPs and applications to coding SIAM J. Comput. 36 4 2006 120 134
2. Eli Ben-Sasson, and Madhu Sudan Robust locally testable codes and products of codes Random Structures Algorithms 28 4 2006 387 402 Preliminary version in APPROX-RANDOM 2004 (Pubitemid 43998384)
3. Eli Ben-Sasson, and Madhu Sudan Short PCPs with polylog query complexity SIAM J. Comput. 38 2 2008 551 607 Preliminary version in STOC 2005
4. Eli Ben-Sasson, Michael Viderman, Composition of semi-LTCs by two-wise tensor products, in: APPROX-RANDOM 2009, pp. 378-391.
5. Eli Ben-Sasson, and Michael Viderman Tensor products of weakly smooth codes are robust Theory Comput. 5 1 2009 239 255
6. Don Coppersmith, and Atri Rudra On the robust testability of tensor products of codes Electron. Colloq. on Comput. Complexity (ECCC) 104 2005
7. Irit Dinur The PCP theorem by gap amplification J. ACM 54 3 2007 241 250 Preliminary version in STOC 2006
8. Irit Dinur, and Omer Reingold Assignment testers: Towards combinatorial proof of the PCP theorem SIAM J. Comput. 36 4 2006 155 164
9. Irit Dinur, Madhu Sudan, Avi Wigderson, Robust local testability of tensor products of LDPC codes, in: APPROX-RANDOM 2006, pp. 304-315. (Pubitemid 44577540)
10. Oded Goldreich Short locally testable codes and proofs (survey) Electron. Colloq. on Comput. Complexity (ECCC) 14 2005
11. Oded Goldreich, and Madhu Sudan Locally testable codes and PCPs of almost linear length J. ACM 53 4 2006 558 655 Preliminary version in FOCS 2002, pp. 13-22 (Pubitemid 44435052)
12. Or Meir On the rectangle method in proofs of robustness of tensor products Electron. Colloq. on Comput. Complexity (ECCC) 14 061 2007
13. Or Meir Combinatorial construction of locally testable codes SIAM J. Comput. 39 2 2009 491 544 Preliminary version appeared in STOC 2008, full version can be retrieved as ECCC TR07-115
14. Florence Jessie MacWilliams, and Neil James Alexander Sloane The Theory of Error Correcting Codes 1988 Elsevier/North-Holland Amsterdam
15. Alexander Polishchuk, Daniel A. Spielman, Nearly-linear size holographic proofs, in: STOC 1994, pp. 194-203.
16. Paul Valiant, The tensor product of two codes is not necessarily robustly testable, in: APPROX-RANDOM 2005, pp. 472-481. (Pubitemid 41480457)
17. R.R. Varshamov Estimate of the number of signals in error correcting codes Dokl. Akad. Nauk 117 1957 739 741
18. Michael Viderman A combination of testability and decodability by tensor products Electron. Colloq. on Comput. Complexity (ECCC) 18 2011 87