Robust locally testable codes and products of codes

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

Volumn 3122, Issue , 2004, Pages 286-297

  Ben Sasson, Eli ^a   Sudan, Madhu ^b  

^a HARVARD UNIVERSITY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; COMBINATORIAL OPTIMIZATION; ERROR CORRECTION; INVERSE PROBLEMS; OPTIMIZATION; QUERY PROCESSING; TENSORS;

ALGEBRAIC PROPERTIES; ERROR CORRECTING CODE; GENERIC CONSTRUCTION; LINEAR ERROR-CORRECTING CODES; LOCALLY TESTABLE CODES; MULTIVARIATE POLYNOMIAL; PROBABILISTICALLY CHECKABLE PROOF; TENSOR PRODUCTS;

CODES (SYMBOLS);

EID: 26944453726     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-27821-4_26     Document Type: Article

References (26)

1. Noga Alon, Tali Kaufman, Michael Krivelevich, Simon Litsyn, and Dana Ron. Testing Reed-Muller codes. Proc. RANDOM 2003, 188-199, 2003.
2. Sanjeev Arora. Probabilistic checking of proofs and the hardness of approximation problems. PhD thesis, University of California at Berkeley, 1994.
3. Sanjeev Arora, Carsten 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.
4. Sanjeev Arora and Shmuel Safra. Probabilistic checking of proofs: A new characterization of NP. Journal of the ACM, 45(1):70-122, January 1998.
5. Sanjeev Arora and Madhu Sudan. Improved low-degree testing and its applications. Proc. STOC97, 485-495, El Paso, Texas, 4-6 May 1997.
6. Lászlá Babai, Lance Fortnow, Leonid A. Levin, and Mario Szegedy. Checking computations in polylogarithmic time. Proc. STOC91, 21-32. 1991.
7. László Babai, Lance Fortnow, and Carsten Lund. Non-deterministic exponential time has two-prover interactive protocols. Computational Complexity, 1(1):3-40, 1991.
8. Mihir Bellare, Don Coppersmith, Johan Håstad, Marcos Kiwi, and Madhu Sudan. Linearity testing over characteristic two. IEEE Transactions on Information Theory, 42(6):1781-1795, November 1996.
9. Mihir Bellare, Shafi Goldwasser, Carsten Lund, and Alex Russell. Efficient probabilistically checkable proofs and applications to approximation. Proc. STOC93, 294-304. ACM, New York, 1993.
10. Mihir Bellare and Madhu Sudan. Improved non-approximability results. Proc. STOC94, 184-193, Montreal, Quebec, Canada, 23-25 May 1994.
11. Eli Ben-Sasson, Oded Goldreich, Prahladh Harsha, Madhu Sudan, and Salil Vadhan. Robust PCPs of proximity, shorter PCPs and applications to coding. Proc. STOC04, (to appear), 2004.
12. Eli Ben-Sasson and Madhu Sudan. Robust Locally Testable Codes and Products of Codes. Available at Electronic Colloquium on Computational Complexity http://eccc.uni-trier.de/eccc-reports/2004/TR04-046/index.html
13. Eli Ben-Sasson, Madhu Sudan, Salil Vadhan, and Avi Wigderson. Randomness efficient low-degree tests and short PCPs via ε-biased sets. Proc. STOC03, 612-621, 2003.
14. Manuel Blum, Michael Luby, and Ronitt Rubinfeld. Self-testing/correcting with applications to numerical problems. Journal of Computer and System Sciences, 47(3):549-595, 1993.
15. Irit Dinur and Omer Reingold. Assignment-Testers: Towards a Combinatorial Proof of the PCP-Theorem. Manuscript, 2004.
16. 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.
17. Katalin Friedl, Zsolt Hatsagi, and Alexander Shen. Low-degree tests. Proc. SODA94, 57-64, 1994.
18. Katalin Friedl and Madhu Sudan. Some improvements to total degree tests. Proc. Israel STCS, 190-198, Tel Aviv, Israel, 4-6 January 1995.
19. Oded Goldreich and Muli Safra. A Combinatorial Consistency Lemma with application to the PCP Theorem. SIAM Jour, on Comp., Volume 29, Number 4, 1132-1154, 1999.
20. Oded Goldreich and Madhu Sudan. Locally testable codes and PCPs of almost-linear length. Proc. FOCS02, Vancouver, Canada, 16-19 November 2002.
21. F. J. MacWilliams and Neil J. A. Sloane. The Theory of Error-Correcting Codes. Elsevier/North-Holland, Amsterdam, 1981.
22. Alexander Polishchuk and Daniel A. Spielman. Nearly linear-size holographic proofs. Proc. STOC94, 194-203, Montreal, Canada, 1994.
23. Ran Raz and Shmuel Safra. A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP. Proc. STOC97, 475-484. ACM Press, 1997.
24. Ronitt Rubinfeld and Madhu Sudan. Robust characterizations of polynomials with applications to program testing. SIAM J. Comp., 25(2):252-271, 1996.
25. Madhu Sudan. Algorithmic introduction to coding theory. Lecture notes, Available from http://theory.csail.mit.edu/~madhu/FT01/, 2001.
26. R. Michael Tanner. A recursive approach to low complexity codes. IEEE Transactions of Information Theory, 27(5):533-547, September 1981.