3-QUERY LOCALLY DECODABLE CODES OF SUBEXPONENTIAL LENGTH

被引：60
|
作者：
Efremenko, Klim [1 ]
机构：
[1] Tel Aviv Univ, Blavatnik Sch Comp Sci, IL-69978 Tel Aviv, Israel
来源：
SIAM JOURNAL ON COMPUTING | 2012年 / 41卷 / 06期
基金：
以色列科学基金会;
关键词：
locally decodable codes; private information retrieval; LOWER BOUNDS; CONSTRUCTIONS;
D O I：
10.1137/090772721
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Locally decodable codes (LDCs) allow one to decode any particular symbol of the input message by making a constant number of queries to a codeword, even if a constant fraction of the codeword is damaged. In a recent work [J. ACM, 55 (2008), article 1], Yekhanin constructs a 3-query LDC with subexponential length. However, this construction requires a conjecture that there are infinitely many Mersenne primes. In this paper, we give the first unconditional constant query LDC construction with subexponential codeword length. In addition, our construction reduces codeword length.
引用
收藏
页码：1694 / 1703
页数：10
相关论文
共 50 条
  • [21] Exponential lower bound for 2-query locally decodable codes via a quantum argument
    Kerenidis, I
    de Wolf, R
    JOURNAL OF COMPUTER AND SYSTEM SCIENCES, 2004, 69 (03) : 395 - 420
  • [22] Locally Testable vs. Locally Decodable Codes
    Kaufman, Tali
    Viderman, Michael
    APPROXIMATION, RANDOMIZATION, AND COMBINATORIAL OPTIMIZATION: ALGORITHMS AND TECHNIQUES, 2010, 6302 : 670 - +
  • [23] Reliable computations based on locally decodable codes
    Romashchenko, A
    STACS 2006, PROCEEDINGS, 2006, 3884 : 537 - 548
  • [24] A Quadratic Lower Bound for Three-Query Linear Locally Decodable Codes over Any Field
    Woodruff, David P.
    APPROXIMATION, RANDOMIZATION, AND COMBINATORIAL OPTIMIZATION: ALGORITHMS AND TECHNIQUES, 2010, 6302 : 766 - 779
  • [25] A Quadratic Lower Bound for Three-Query Linear Locally Decodable Codes over Any Field
    David P. Woodruff
    Journal of Computer Science and Technology, 2012, 27 : 678 - 686
  • [26] Sound 3-query PCPPs are long
    Ben-Sasson, Eli
    Harsha, Prahladh
    Lachish, Oded
    Matsliah, Arie
    ACM Transactions on Computation Theory, 2009, 1 (02)
  • [27] Lower bounds for adaptive locally decodable codes
    Deshpande, A
    Jain, R
    Kavitha, T
    Lokam, SV
    Radhakrishnan, J
    RANDOM STRUCTURES & ALGORITHMS, 2005, 27 (03) : 358 - 378
  • [28] Better lower bounds for locally decodable codes
    Deshpande, A
    Jain, R
    Kavitha, T
    Lokam, SV
    Radhakrishnan, J
    17TH ANNUAL IEEE CONFERENCE ON COMPUTATIONAL COMPLEXITY, PROCEEDINGS, 2002, : 184 - 193
  • [29] From Irreducible Representations to Locally Decodable Codes
    Efremenko, Klim
    STOC'12: PROCEEDINGS OF THE 2012 ACM SYMPOSIUM ON THEORY OF COMPUTING, 2012, : 327 - 337
  • [30] Using T-Codes as Locally Decodable Source Codes
    Speidel, Ulrich
    Gulliver, T. Aaron
    Makhdoumi, Ali
    Medard, Muriel
    2014 IEEE INFORMATION THEORY WORKSHOP (ITW), 2014, : 217 - 221
12345