Query-Efficient Locally Decodable Codes of Subexponential Length

A k-query locally decodable code (LDC) C : n N encodes each message x into a codeword C(x) such that each symbol of x can be probabilistically recovered by querying only k coordinates of C(x), even after a constant fraction of the coordinates have been corrupted. Yekhanin (2008) constructed a 3-query LDC of subexponential length, N = exp(exp(O(log n/ log log n))), under the assumption that there are infinitely many Mersenne primes. Efremenko (2009) constructed a 3-query LDC of length N2 = exp(exp(O( log n log log n))) with no assumption, and a 2r-query LDC of length Nr = exp(exp(O( r log n(log log n)r-1))), for every integer r 2. Itoh and Suzuki (2010) gave a composition method in Efremenko's framework and constructed a 3

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Yeow Meng Chee, Tao Feng, San Ling, Huaxiong Wang, Liang Feng Zhang
• Keywords: Composite Numbers, CORR 2010, Education, Integer, Length Nr