TY - GEN

T1 - 3-query locally decodable codes of subexponential length

AU - Efremenko, Klim

PY - 2009/11/9

Y1 - 2009/11/9

N2 - 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))).

AB - 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))).

KW - Locally decodable codes

KW - Private information retrieval schemes

UR - http://www.scopus.com/inward/record.url?scp=70350642094&partnerID=8YFLogxK

U2 - 10.1145/1536414.1536422

DO - 10.1145/1536414.1536422

M3 - Conference contribution

AN - SCOPUS:70350642094

SN - 9781605585062

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 39

EP - 44

BT - STOC'09 - Proceedings of the 2009 ACM International Symposium on Theory of Computing

T2 - 41st Annual ACM Symposium on Theory of Computing, STOC '09

Y2 - 31 May 2009 through 2 June 2009

ER -