Locally Testable Codes Require Redundant Testers
نویسندگان
چکیده
منابع مشابه
Universal Locally Testable Codes
We initiate a study of “universal locally testable codes” (universal-LTCs). These codes admit local tests for membership in numerous possible subcodes, allowing for testing properties of the encoded message. More precisely, a universal-LTC C : {0, 1} → {0, 1} for a family of functions F = { fi : {0, 1} → {0, 1} } i∈[M ] is a code such that for every i ∈ [M ] the subcode {C(x) : fi(x) = 1} is lo...
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An error-correcting code is said to be locally testable if it has an efficient spot-checking procedure that can distinguish codewords from strings that are far from every codeword, looking at very few locations of the input in doing so. Locally testable codes (LTCs) have generated a lot of interest over the years, in large part due to their connection to Probabilistically checkable proofs (PCPs...
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A locally testable code is a code defined by a robust set of local constraints. Namely, the distance of a vector from the code is well approximated by the fraction of local constraints that it violates. A constraint graph of an LTC is a graph whose vertices are labeled by the coordinates of the code, and vertex i is adjacent to j whenever they occur together in a constraint. We study the relati...
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We study the relation between locally testable and locally decodable codes. Locally testable codes (LTCs) are error-correcting codes for which membership of a given word in the code can be tested probabilistically by examining it in very few locations. Locally decodable codes (LDCs) allow to recover each message entry with high probability by reading only a few entries of a slightly corrupted c...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2010
ISSN: 0097-5397,1095-7111
DOI: 10.1137/090779875