Query-Efficient Locally Decodable Codes of Subexponential Length
نویسندگان
چکیده
منابع مشابه
Query-Efficient Locally Decodable Codes of Subexponential Length
A k-query locally decodable code (LDC) C : Σn → ΓN 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 ...
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A k-query locally decodable code (LDC) C : Σn → ΓN 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 ...
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A (k, δ, ε)-locally decodable code C : Fnq → F N q is an error-correcting code that encodes each message ~x = (x1, x2, . . . , xn) ∈ F n q to a codeword C(~x) ∈ F N q and has the following property: For any ~y ∈ Fq such that d(~y, C(~x)) ≤ δN and each 1 ≤ i ≤ n, the symbol xi of ~x can be recovered with probability at least 1−ε by a randomized decoding algorithm looking only at k coordinates of...
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A (q, δ, )-locally decodable code (LDC) C : {0, 1} → {0, 1} is an encoding from n-bit strings to m-bit strings such that each bit xk can be recovered with probability at least 1 2 + from C(x) by a randomized algorithm that queries only q positions of C(x), even if up to δm positions of C(x) are corrupted. If C is a linear map, then the LDC is linear. We give improved constructions of LDCs in te...
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ژورنال
عنوان ژورنال: computational complexity
سال: 2011
ISSN: 1016-3328,1420-8954
DOI: 10.1007/s00037-011-0017-1