Proximity Gaps Conjecture Fails Near Capacity over Prime Fields
Information Theory
2026-04-14 v1 Cryptography and Security
math.IT
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 below the capacity rate of the code, where is the length of the code.
Cite
@article{arxiv.2604.09724,
title = {Proximity Gaps Conjecture Fails Near Capacity over Prime Fields},
author = {Antonio Kambiré},
journal= {arXiv preprint arXiv:2604.09724},
year = {2026}
}