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Volumn , Issue , 2009, Pages 181-190

Extensions to the method of multiplicities, with applications to Kakeya sets and mergers

Author keywords

Extractors; Polynomial method; Randomness

Indexed keywords

COMBINATORICS; EXPONENTIAL FACTORS; FINITE FIELDS; FINITE SUBSETS; HIGH MULTIPLICITY; INPUT VARIABLES; INTERPOLATING POLYNOMIALS; LOW DEGREE; MIN-ENTROPY; POLYNOMIAL METHODS; RANDOM POINTS; RANDOM SEEDS; RANDOMNESS EXTRACTORS;

EID: 77952402919     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2009.40     Document Type: Conference Paper
Times cited : (66)

References (22)
  • 1
    • 77952373788 scopus 로고    scopus 로고
    • A combinatorial bound on the list size
    • California Institute of Technology
    • Yuval Cassuto and Jehoshua Bruck. A combinatorial bound on the list size. Paradise Laboratory Technical report, California Institute of Technology, 2004.
    • (2004) Paradise Laboratory Technical Report
    • Cassuto, Y.1    Bruck, J.2
  • 2
    • 84871964246 scopus 로고    scopus 로고
    • Extensions to the method of multiplicities, with applications to Kakeya sets and mergers
    • Revision 02, May
    • Zeev Dvir, Swastik Kopparty, Shubhangi Saraf, Madhu Sudan. Extensions to the method of multiplicities, with applications to Kakeya sets and mergers. ECCC Technical report TR09-004, Revision 02, May 2009.
    • (2009) ECCC Technical Report TR09-004
    • Dvir, Z.1    Kopparty, S.2    Saraf, S.3    Sudan, M.4
  • 3
    • 34249018298 scopus 로고    scopus 로고
    • An improved analysis of linear mergers
    • (Extended abstract appeared in RANDOM 2005)
    • Z. Dvir and A. Shpilka. An improved analysis of linear mergers. Comput. Complex., 16(1):34-59, 2007. (Extended abstract appeared in RANDOM 2005).
    • (2007) Comput. Complex. , vol.16 , Issue.1 , pp. 34-59
    • Dvir, Z.1    Shpilka, A.2
  • 4
    • 57949104082 scopus 로고    scopus 로고
    • On the size of Kakeya sets in finite fields
    • (to appear)
    • Z. Dvir. On the size of Kakeya sets in finite fields. J. AMS (to appear), 2008.
    • (2008) J. AMS
    • Dvir, Z.1
  • 5
    • 57949092809 scopus 로고    scopus 로고
    • Kakeya sets, new mergers and old extractors
    • IEEE Computer Society
    • Zeev Dvir and Avi Wigderson. Kakeya sets, new mergers and old extractors. In FOCS, pages 625-633. IEEE Computer Society, 2008.
    • (2008) FOCS , pp. 625-633
    • Dvir, Z.1    Wigderson, A.2
  • 6
    • 33748105468 scopus 로고    scopus 로고
    • Explicit capacity-achieving list-decodable codes
    • Jon M. Kleinberg, editor ACM
    • Venkatesan Guruswami and Atri Rudra. Explicit capacity-achieving list-decodable codes. In Jon M. Kleinberg, editor, STOC, pages 1-10. ACM, 2006.
    • (2006) STOC , pp. 1-10
    • Guruswami, V.1    Rudra, A.2
  • 7
    • 0033183669 scopus 로고    scopus 로고
    • Improved decoding of Reed-Solomon and algebraic-geometric codes
    • Venkatesan Guruswami and Madhu Sudan. Improved decoding of Reed-Solomon and algebraic-geometric codes. IEEE Transactions on Information Theory, 45:1757-1767, 1999.
    • (1999) IEEE Transactions on Information Theory , vol.45 , pp. 1757-1767
    • Guruswami, V.1    Sudan, M.2
  • 8
    • 34748894441 scopus 로고    scopus 로고
    • Unbalanced expanders and randomness extractors from Parvaresh-Vardy codes
    • IEEE Computer Society
    • Venkatesan Guruswami, Christopher Umans, and Salil P. Vadhan. Unbalanced expanders and randomness extractors from Parvaresh-Vardy codes. In IEEE Conference on Computational Complexity, pages 96-108. IEEE Computer Society, 2007.
    • (2007) IEEE Conference on Computational Complexity , pp. 96-108
    • Guruswami, V.1    Umans, C.2    Vadhan, S.P.3
  • 11
    • 33646831750 scopus 로고    scopus 로고
    • Correcting errors beyond the Guruswami-Sudan radius in polynomial time
    • IEEE Computer Society
    • Farzad Parvaresh and Alexander Vardy. Correcting errors beyond the Guruswami-Sudan radius in polynomial time. In FOCS, pages 285-294. IEEE Computer Society, 2005.
    • (2005) FOCS , pp. 285-294
    • Parvaresh, F.1    Vardy, A.2
  • 15
    • 78149414388 scopus 로고    scopus 로고
    • Improved lower bound on the size of Kakeya sets over finite fields
    • Shubhangi Saraf and Madhu Sudan. Improved lower bound on the size of Kakeya sets over finite fields. Analysis and PDE (to appear), 2008.
    • (2008) Analysis and PDE (to Appear)
    • Saraf, S.1    Sudan, M.2
  • 16
    • 0031097176 scopus 로고    scopus 로고
    • Decoding of Reed-Solomon codes beyond the error-correction bound
    • Madhu Sudan. Decoding of Reed-Solomon codes beyond the error-correction bound. Journal of Complexity, 13(1):180-193, 1997.
    • (1997) Journal of Complexity , vol.13 , Issue.1 , pp. 180-193
    • Sudan, M.1
  • 18
    • 1842700522 scopus 로고    scopus 로고
    • PhD Thesis, The Hebrew University, Jerusalem, Israel
    • A. Ta-Shma. Refining Randomness. PhD Thesis, The Hebrew University, Jerusalem, Israel, 1996.
    • (1996) Refining Randomness
    • Ta-Shma, A.1
  • 20
    • 0040707391 scopus 로고    scopus 로고
    • Expanders that beat the eigenvalue bound: Explicit construction and applications
    • Avi Wigderson and David Zuckerman. Expanders that beat the eigenvalue bound: explicit construction and applications. Combinatorica, 19(1):125-138, 1999.
    • (1999) Combinatorica , vol.19 , Issue.1 , pp. 125-138
    • Wigderson, A.1    Zuckerman, D.2
  • 21
    • 0002849466 scopus 로고    scopus 로고
    • Recent work connected with the Kakeya problem
    • Princeton, NJ
    • T. Wolff. Recent work connected with the Kakeya problem. In Prospects in Mathematics, pages 129-162. Princeton, NJ, 1999.
    • (1999) Prospects in Mathematics , pp. 129-162
    • Wolff, T.1
  • 22
    • 43849088675 scopus 로고    scopus 로고
    • Linear degree extractors and the in-approximability of max clique and chromatic number
    • David Zuckerman. Linear degree extractors and the in-approximability of max clique and chromatic number. Theory of Computing, 3(1):103-128, 2007.
    • (2007) Theory of Computing , vol.3 , Issue.1 , pp. 103-128
    • Zuckerman, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.