The Coxeter Code Minimum Distance Conjecture
Coble and Barg introduced binary Coxeter codes, the span of indicators of standard cosets of fixed rank in a finite Coxeter system, generalizing Reed-Muller codes, and proposed a conjectural value for the minimum distance of a general Coxeter code. The conjecture is true, and it yields a decoding consequence.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Argument
- Field
- Coding theory
- Posed by
- Nolan Coble, Alexander Barg
- Year posed
- 2025
- Years open
- 1y
- Solved
- 2026-07-12
- Model
- ChatGPT-5.4, Claude Sonnet 4.6
- Vendor
- OpenAI / Anthropic
- Collaborators
- Alexander Barg, Qendrim R. Gashi, Tianyuan Xu
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 7 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The authors say the models were used as exploratory tools in connection with the problem, and bound that use explicitly: brainstorming, discussion of possible approaches, and preliminary checking of ideas.
Verification
arXiv preprint; not yet peer-reviewed.