ProbXiv
sign in
Problem archiveProblem record

The Coxeter Code Minimum Distance Conjecture

Combinatorics · posed by Nolan Coble, Alexander Barg, 2025 · solved

1 comment

Statement

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.

Record

Source
Added

Comments

No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Alexander Barg, Qendrim R. Gashi and Tianyuan Xu, using ChatGPT-5.4, Claude Sonnet 4.6

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    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.

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.