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#DinurEvraLivneLubotzkyMozes-3
"1 Introduction
A locally testable code (LTC) is an #ErrorCorrectingCode that has a property-tester. The tester reads 𝑞 bits (randomly - but not necessarily uniformly chosen) from a given word, and rejects words with probability proportional to
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"1 Introduction
A locally testable code (LTC) is an #ErrorCorrectingCode that has a property-tester. The tester reads 𝑞 bits (randomly - but not necessarily uniformly chosen) from a given word, and rejects words with probability proportional to
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>their distance from the code. The parameter 𝑞 is called the locality of the tester.
A random code has, with high probability, constant rate and distance, but locality that is proportional to the length. This is true even for random #LDPC codes [BHR05], and
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A random code has, with high probability, constant rate and distance, but locality that is proportional to the length. This is true even for random #LDPC codes [BHR05], and
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>a priori the mere existence of codes with constant locality is not obvious. The first LTCs appear implicitly in works on #ProgramChecking [BLR90] and on #ProbabilisticallyCheckableProofs (PCPs) [BFL91, LFKN92, BFLS91, AS98, ALM+98].
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