Years and Authors of Summarized Original Work
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1990; Blum, Luby, Rubinfeld
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2002; Goldreich, Sudan
Problem Definition
Locally testable codes (LTC) are error-correcting codes that support algorithms which can distinguish valid codewords from words that are “far” from all codewords by probing a given word only at a sublinear (typically constant) number of locations. LTCs are useful in the following scenario. Suppose data is transmitted by encoding it using a LTC. Then, one could check if the received data is nearly uncorrupted or has been considerably corrupted by making very few probes into the received data.
An error-correcting code \(\mathcal{C} :\{ 0,1\}^{k} \rightarrow \{ 0,1\}^{n}\) is a function mapping k-bit messages to n-bit codewords. The ratio k∕n is referred to as the rate of the code \(\mathcal{C}\). The Hamming distance between two n-bit strings x and y, denoted by Δ(x, y), is the number of locations where x and y disagree, i.e., Δ(x, y) = { i ∈ [n]∣x i ≠ y i }. The relative...
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Recommended Reading
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Harsha, P. (2016). Locally Testable Codes. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_707
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