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Volumn 35, Issue 2, 2009, Pages 163-193

Testing low-degree polynomials over prime fields

Author keywords

Generalized Reed Muller code; Local correction; Local testing; Polynomials

Indexed keywords


EID: 68349133177     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20262     Document Type: Article
Times cited : (39)

References (24)
  • 4
    • 0032058198 scopus 로고    scopus 로고
    • Proof verification and the intractibility of approximation problems
    • S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy, Proof verification and the intractibility of approximation problems, J ACM 45 (1998), 501-555.
    • (1998) J ACM , vol.45 , pp. 501-555
    • Arora, S.1    Lund, C.2    Motwani, R.3    Sudan, M.4    Szegedy, M.5
  • 5
    • 0031651077 scopus 로고    scopus 로고
    • Probabilistic checking of proofs: A new characterization of NP
    • S. Arora and S. Safra, Probabilistic checking of proofs: A new characterization of NP, J ACM 45 (1998), 70-122.
    • (1998) J ACM , vol.45 , pp. 70-122
    • Arora, S.1    Safra, S.2
  • 6
    • 0347589496 scopus 로고    scopus 로고
    • Improved low-degree testing and its applications
    • S. Arora and M. Sudan, Improved low-degree testing and its applications, Combinatorica 23 (2003), 365-426.
    • (2003) Combinatorica , vol.23 , pp. 365-426
    • Arora, S.1    Sudan, M.2
  • 7
    • 0002771903 scopus 로고
    • Non-deterministic exponential time has two prover interactive protocols
    • L. Babai, L. Fortnow, and C. Lund, Non-deterministic exponential time has two prover interactive protocols, Computational Complexity 1 (1991), 3-40.
    • (1991) Computational Complexity , vol.1 , pp. 3-40
    • Babai, L.1    Fortnow, L.2    Lund, C.3
  • 9
    • 0000619172 scopus 로고
    • Self-testing/correcting with applications to numerical problems
    • M. Blum, M. Luby, and R. Rubinfeld, Self-testing/correcting with applications to numerical problems, J Comput Syst Sci 47 (1993), 549-595.
    • (1993) J Comput Syst Sci , vol.47 , pp. 549-595
    • Blum, M.1    Luby, M.2    Rubinfeld, R.3
  • 11
    • 33745711597 scopus 로고    scopus 로고
    • Robust locally testable codes and products of codes
    • E. Ben-Sasson and M. Sudan, Robust locally testable codes and products of codes, Random Struct Algorithms 28 (2006), 387-402.
    • (2006) Random Struct Algorithms , vol.28 , pp. 387-402
    • Ben-Sasson, E.1    Sudan, M.2
  • 12
    • 34250101655 scopus 로고
    • Functions and polynomials in vector spaces
    • S. D. Cohen, Functions and polynomials in vector spaces, Archiv der Mathematik IT-14 (1987), 409-419.
    • (1987) Archiv der Mathematik IT-14 , pp. 409-419
    • Cohen, S.D.1
  • 13
    • 0000220711 scopus 로고
    • On cyclic codes that are invariant under the general linear group
    • P. Delsarte, On cyclic codes that are invariant under the general linear group, IEEE Trans Inf Theory 16 (1970), 760-769.
    • (1970) IEEE Trans Inf Theory , vol.16 , pp. 760-769
    • Delsarte, P.1
  • 14
    • 0014821518 scopus 로고
    • On generalized Reed-Muller codes and their relatives
    • P. Delsarte, J. M. Goethals, and F. J. MacWillams, On generalized Reed-Muller codes and their relatives, Inf Control 16 (1970), 403-442.
    • (1970) Inf Control , vol.16 , pp. 403-442
    • Delsarte, P.1    Goethals, J.M.2    MacWillams, F.J.3
  • 15
    • 0034271895 scopus 로고    scopus 로고
    • Minimum-weight codewords as generators of generalized Reed-Muller codes
    • P. Ding and J. D. Key, Minimum-weight codewords as generators of generalized Reed-Muller codes, IEEE Trans Inf Theory 46 (2000), 2152-2158.
    • (2000) IEEE Trans Inf Theory , vol.46 , pp. 2152-2158
    • Ding, P.1    Key, J.D.2
  • 16
    • 0030100766 scopus 로고    scopus 로고
    • Interactive proofs and the hardness of approximating cliques
    • U. Feige, S. Goldwasser, L. Lovász, S. Safra, and M. Szegedy, Interactive proofs and the hardness of approximating cliques, J ACM 43 (1996), 268-292.
    • (1996) J ACM , vol.43 , pp. 268-292
    • Feige, U.1    Goldwasser, S.2    Lovász, L.3    Safra, S.4    Szegedy, M.5
  • 21
    • 34250862184 scopus 로고    scopus 로고
    • Testing polynomials over general fields
    • T. Kaufman and D. Ron, Testing polynomials over general fields, SIAM J Comput 36 (2006), 779-802.
    • (2006) SIAM J Comput , vol.36 , pp. 779-802
    • Kaufman, T.1    Ron, D.2
  • 22
    • 68349138891 scopus 로고    scopus 로고
    • Error-correcting Codes: Local Testing, List Decoding, and Applications
    • PhD thesis, University of Texas at Austin, Austin
    • A. C. Patthak, Error-correcting Codes: Local Testing, List Decoding, and Applications, PhD thesis, University of Texas at Austin, Austin, 2007.
    • (2007)
    • Patthak, A.C.1
  • 23
    • 0030128622 scopus 로고    scopus 로고
    • Robust characterizations of polynomials with applications to program testing
    • R. Rubinfeld and M. Sudan, Robust characterizations of polynomials with applications to program testing, SIAM J Comput 25 (1996), 252-271.
    • (1996) SIAM J Comput , vol.25 , pp. 252-271
    • Rubinfeld, R.1    Sudan, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.