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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.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Jul 12, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-assisted. Imported under CC BY 4.0.

Canonical aliases: The Coxeter Code Minimum Distance Conjecture · Coxeter codes

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Alexander Barg
human · human collaborator

Qendrim R. Gashi
human · human collaborator

Tianyuan Xu
human · human collaborator

Claude Sonnet 4.6
model · ai model contributor · OpenAI / Anthropic

ChatGPT-5.4
model · ai model contributor · OpenAI / Anthropic

Lineage and corrections

This event attributed to Alexander Barg

This event attributed to Qendrim R. Gashi

This event attributed to Tianyuan Xu

This event attributed to ChatGPT-5.4

This event attributed to Claude Sonnet 4.6

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