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SUMMARY:A stronger bound for linear 3-LCC - Tal Yankovitz (Tel-Aviv Univer
 sity)
DTSTART:20250128T140000Z
DTEND:20250128T150000Z
UID:TALK224962@talks.cam.ac.uk
CONTACT:Tom Gur
DESCRIPTION: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.
 \n\nIn a breakthrough result Kothari and Manohar (STOC 2024) showed that f
 or linear 3-LCC n=2^Ω(k^1/8) . In this work we prove that n=2^Ω(k^1/4) .
  As Reed-Muller codes yield 3-LCC with n=2^O(k^1/2) \, this brings us clos
 er to closing the gap. Moreover\, in the special case of design-LCC (into 
 which Reed-Muller fall) the bound we get is n=2^Ω(k^1/3).
LOCATION:Computer Laboratory\, William Gates Building\, Room FW09
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