Abstract:
A q-locally correctable code (LCC) C:\{0,1\}^{k}\rightarrow \{0,1\}^{n} is a code in which it is possible to correct every bit of a (not too) corrupted codeword by maki...Show MoreMetadata
Abstract:
A q-locally correctable code (LCC) C:\{0,1\}^{k}\rightarrow \{0,1\}^{n} is a code in which it is possible to correct every bit of a (not too) corrupted codeword by making at most q queries to the word. The cases in which q is constant are of special interest, and so are the cases that C is linear. In a breakthrough result Kothari and Manohar (STOC 2024) showed that for linear 3-LCC n=2^{\Omega(k^{1/8})}. In this work we prove that n=2^{\Omega(k^{1/4})}. As Reed-Muller codes yield 3-LCC with n=2^{O(k^{1/2})}, this brings us closer to closing the gap. Moreover, in the special case of design-LCC (into which Reed-Muller fall) the bound we get is n=2^{\Omega(k^{1/3})}.
Date of Conference: 27-30 October 2024
Date Added to IEEE Xplore: 29 November 2024
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