3-query locally decodable codes of subexponential length

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Abstract

Locally Decodable Codes (LDC) 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 [Yek08] Yekhanin constructs a 3-query LDC with sub-exponential length of size exp(exp(O( log n/log log n ))). 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 sub-exponential codeword length. In addition our construction reduces the codeword length. We give a construction of a 3-query LDC with codeword length exp(exp(O(√log n log log n))). Our construction also can be extended to a higher number of queries. We give a 2r-query LDC with length of exp(exp(O( r√log n(log log n)r-1))).

Original languageEnglish
Title of host publicationSTOC'09 - Proceedings of the 2009 ACM International Symposium on Theory of Computing
Pages39-44
Number of pages6
DOIs
StatePublished - 9 Nov 2009
Externally publishedYes
Event41st Annual ACM Symposium on Theory of Computing, STOC '09 - Bethesda, MD, United States
Duration: 31 May 20092 Jun 2009

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference41st Annual ACM Symposium on Theory of Computing, STOC '09
Country/TerritoryUnited States
CityBethesda, MD
Period31/05/092/06/09

Keywords

  • Locally decodable codes
  • Private information retrieval schemes

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