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  "problem_id": "vibemathed:coxeter-code-minimum-distance",
  "title": "The Coxeter Code Minimum Distance Conjecture",
  "canonical_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.",
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      "title": "arXiv:2607.10774 - Minimum distance and decoding of Coxeter codes",
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        "Alexander Barg",
        "Qendrim R. Gashi",
        "Tianyuan Xu"
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