Robust local testability of tensor products of LDPC codes

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4110 LNCS, Issue , 2006, Pages 304-315

  Dinur, Irit ^a   Sudan, Madhu ^b   Wigderson, Avi ^c  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMBINATORIAL MATHEMATICS; MATRIX ALGEBRA; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS); TENSORS;

EXPANDER CODES; LINEAR CODES; TENSOR PRODUCTS;

BINARY CODES;

EID: 33750077781     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11830924_29     Document Type: Conference Paper

References (13)

1. Sanjeev Arora, Garsten Lund, Rajeev Motwani, Madhu Sudan, and Mario Szegedy. Proof verification and the hardness of approximation problems. Journal of the ACM, 45(3):501-555, May 1998.
2. Sanjeev Arora and Shmuel Safra. Probabilistic checking of proofs: A new characterization of NP. Journal of the ACM, 45(1):70-122, January 1998.
3. Eli Ben-Sasson, Oded Goldreich, Prahladh Harsha, Madhu Sudan, and Salil Vadhan. Robust PCPs of proximity, shorter PCPs and applications to coding. In Proceedings of the 36th Annual ACM Symposium on Theory of Computing, page (to appear), 2004.
4. Eli Ben-Sasson, Oded Goldriech, Prahladh Harsha, Madhu Sudan, and Salil Vadhan. Short PCPs verifiable in polylogarithmic time. In Proceedings of the Twelfth Annual IEEE Conference on Computational Complexity, pages 120-134, June 12-15 2005.
5. E. Ben-Sasson and P. Harsha and S. Raskhodnikova, Some 3CNF properties are hard to test. In SIAM Journal on Computing, 35(1):1-21.
6. E. Ben-Sasson and M. Sudan. Robust locally testable codes and products of codes. In Proc. RANDOM: International Workshop on Randomization and Approximation Techniques in Computer Science, pages 286-297, 2004.
7. Eli Ben-Sasson and Madhu Sudan. Short PCPs with poly-log rate and query complexity. In Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pages 266-275, 2005.
8. Eli Ben-Sasson, Madhu Sudan, Salil Vadhan, and Avi Wigderson. Randomness efficient low-degree tests and short PCPs via e-biased sets. In Proceedings of the 35th Annual ACM Symposium on Theory of Computing, pages 612-621, 2003.
9. D. Coppersmith and A. Rudra. On the robust testability of product of codes. ECCC TR05-104, 2005.
10. Irit Dinur. The PCP theorem by gap amplification. In Proceedings of the 38th Annual ACM Symposium on Theory of Computing, pages 241-250, 2006.
11. Uriel Feige, Shafi Goldwasser, Laszlo Lovasz, Shmuel Safra, and Mario Szegedy. Interactive proofs and the hardness of approximating cliques. Journal of the ACM, 43(2):268-292, 1996.
12. O. Goldreich and M. Sudan. Locally testable codes and PCPs of almost-linear length. In Proc. 43rd IEEE Symp. on Foundations of Computer Science, pages 13-22, 2002.
13. P. Valiant. The tensor product of two codes is not necessarily robustly testable. In APPROX-RANDOM, pages 472-481, 2005.