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About this paper
Vinayak M. Kumar, Ray Li, Jonathan Mosheiff, Gilad Shavit
The authors characterize threshold locations for increasing b-local properties of uniformly random linear codes over every field size. They optimize a union bound over covers of witnesses, obtaining a probability threshold between the expectation threshold and 2b+2 dimensions above it. For decreasing properties, the result applies to failure witnesses; conditional transfer to suitable ensembles loses O(b/n) in rate when b=o(n).
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