cs.ITcs.CR
Proximity Gaps Conjecture Fails Near Capacity over Prime Fields
Apr 9, 2026
AI Summarygemma4:e4b
The paper proves that the proximity gaps conjecture fails for a specific family of Reed-Solomon codes near their capacity rate, specifically at radii $O(1/ ext{log } n)$ below capacity.
Abstract
More Like ThisIn this report we flesh out a sketch by Krachun and Kazanin to prove that for a certain family of Reed-Solomon codes, proximity gaps fail at radii that are $O(1/\log n)$ below the capacity rate of the code, where $n$ is the length of the code.