Improved Constructions for 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, 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 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 (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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We prove exponential lower bounds on the length of 2-query locally decodable codes. Goldreich et al. recently proved such bounds for the special case of linear locally decodable codes. Our proof shows that a 2-query locally decodable code can be decoded with only 1 quantum query, and then proves an exponential lower bound for such 1-query locally quantum-decodable codes. We also exhibit q-query...
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ژورنال
عنوان ژورنال: IEICE Transactions on Information and Systems
سال: 2010
ISSN: 0916-8532,1745-1361
DOI: 10.1587/transinf.e93.d.263