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Tuesday 28 January 2025, 14:00-15:00
A stronger bound for linear 3-LCC
- 👤 Speaker: Tal Yankovitz (Tel-Aviv University) 🔗 Website
- 📅 Date & Time: Tuesday 28 January 2025, 14:00 - 15:00
- 📍 Venue: Computer Laboratory, William Gates Building, Room FW09
Abstract
A q-locally correctable code (LCC) C:{0,1}k->{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=2Ω(k1/8) . In this work we prove that n=2Ω(k1/4) . As Reed-Muller codes yield 3-LCC with n=2O(k1/2) , 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=2Ω(k1/3).
Series This talk is part of the Algorithms and Complexity Seminar series.
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