2011 IEEE 26th Annual Conference on Computational Complexity 2011
DOI: 10.1109/ccc.2011.9
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Towards Lower Bounds on Locally Testable Codes via Density Arguments

Abstract: The main open problem in the area of locally testable codes (LTCs) is whether there exists an asymptotically good family of LTCs and to resolve this question it suffices to consider the case of query complexity 3. We argue that to refute the existence of such an asymptotically good family one should prove that the number of dual codewords of weight at most 3 is super-linear in the blocklength of the code.The main technical contribution of this paper is an improvement of the combinatorial lemma of Goldreich et … Show more

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