The Coxeter Code Minimum Distance Conjecture
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.
Context
A conjectural minimum distance proposed in the paper that introduced the codes; recent and specialized, though Reed-Muller codes give it wider context.
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