2009
DOI: 10.1137/080729967
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Combinatorial Construction of Locally Testable Codes

Abstract: An error correcting code is said to be locally testable if there is a test that checks whether a given string is a codeword, or rather far from the code, by reading only a constant number of symbols of the string. While the best known construction of LTCs by Ben-Sasson and Sudan (STOC 2005) and Dinur (J. ACM 54(3)) achieves very ecient parameters, it relies heavily on algebraic tools and on PCP machinery. In this work we present a new and arguably simpler construction of LTCs that is purely combinatorial, doe… Show more

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Cited by 41 publications
(38 citation statements)
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“…Moreover, in the area of LTCs we usually require δ(C)/3. E.g., all known constructions of LTCs satisfy this requirement (see e.g., [10], [12], [20], [23], [24], [30]). On the other side, if for all constants q, > 0 the code C is not (q, , δ(C)/3)-LTC we say that C is not locally testable (see e.g., [4], [8], [25]).…”
Section: A Ltcs and Ldcsmentioning
confidence: 96%
“…Moreover, in the area of LTCs we usually require δ(C)/3. E.g., all known constructions of LTCs satisfy this requirement (see e.g., [10], [12], [20], [23], [24], [30]). On the other side, if for all constants q, > 0 the code C is not (q, , δ(C)/3)-LTC we say that C is not locally testable (see e.g., [4], [8], [25]).…”
Section: A Ltcs and Ldcsmentioning
confidence: 96%
“…Moreover, in the area of LTCs we usually require δ(C )/3. For example, all known constructions of LTCs satisfy this requirement, see (Ben-Sasson & Sudan 2008;Dinur 2007;Kaufman & Sudan 2007Meir 2009)). On the other side, if for all constants q, > 0 the code C is not (q, , δ(C )/3)-LTC we say that C is not locally testable (Babai et al 2005;Kaufman & Viderman 2010).…”
Section: Ltcs and Ldcsmentioning
confidence: 99%
“…We point out all known constructions of LTCs seem to be dense and natural, although the best known LTCs (e.g. Ben-Sasson & Sudan 2008;Dinur 2007;Meir 2009) are not regular but still seem to be dense and natural. Conjecture 3.11 (3-query LTCs are natural and dense).…”
Section: Dense Natural and Regular Ltcs Cannot Be Asymptotically Goodmentioning
confidence: 99%
“…We end this section by pointing out that recently, tensor codes have played a role in the combinatorial construction by Meir [13] of quasilinear length locally testable codes. Better base codes may result in LTCs with improved rate, hence the importance in broadening the class of base codes that can be used to construct robustly testable tensor codes.…”
Section: Test For R ⊗Cmentioning
confidence: 99%