Proximity Gaps Conjecture Fails Near Capacity over Prime Fields

arXiv:2604.09724v1 Announce Type: new
Abstract: In 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.