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
  • [1] 3-Query Locally Decodable Codes of Subexponential Length
    Efremenko, Klim
    STOC'09: PROCEEDINGS OF THE 2009 ACM SYMPOSIUM ON THEORY OF COMPUTING, 2009, : 39 - 44
  • [2] Towards 3-query locally decodable codes of subexponential length
    Yekhanin, Sergey
    JOURNAL OF THE ACM, 2008, 55 (01)
  • [3] Towards 3-Query Locally Decodable Codes of Subexponential Length
    Yekhanin, Sergey
    STOC 07: PROCEEDINGS OF THE 39TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING, 2007, : 266 - 274
  • [4] Query-Efficient Locally Decodable Codes of Subexponential Length
    Yeow Meng Chee
    Tao Feng
    San Ling
    Huaxiong Wang
    Liang Feng Zhang
    computational complexity, 2013, 22 : 159 - 189
  • [5] Query-Efficient Locally Decodable Codes of Subexponential Length
    Chee, Yeow Meng
    Feng, Tao
    Ling, San
    Wang, Huaxiong
    Zhang, Liang Feng
    COMPUTATIONAL COMPLEXITY, 2013, 22 (01) : 159 - 189
  • [6] Improved Constructions for Query-Efficient Locally Decodable Codes of Subexponential Length
    Itoh, Toshiya
    Suzuki, Yasuhiro
    IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS, 2010, E93D (02): : 263 - 270
  • [7] A Near-Cubic Lower Bound for 3-Query Locally Decodable Codes from Semirandom CSP Refutation
    Alrabiah, Omar
    Guruswami, Venkatesan
    Kothari, Pravesh K.
    Manohar, Peter
    PROCEEDINGS OF THE 55TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING, STOC 2023, 2023, : 1438 - 1448
  • [8] An Exponential Lower Bound for Linear 3-Query Locally Correctable Codes
    Kothari, Pravesh K.
    Manohar, Peter
    PROCEEDINGS OF THE 56TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING, STOC 2024, 2024, : 776 - 787
  • [9] Three Query Locally Decodable Codes with Higher Correctness Require Exponential Length
    Gal, Anna
    Mills, Andrew
    28TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS 2011), 2011, 9 : 673 - 684
  • [10] Three-query locally decodable codes with higher correctness require exponential length
    Gal, Anna
    Mills, Andrew
    ACM Transactions on Computation Theory, 2012, 3 (02)
12345