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Hierarchical models, marginal polytopes, and linear codes. (English) Zbl 1167.94340
Summary: We explore a connection between binary hierarchical models, their marginal polytopes, and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.

94B05 Linear codes (general theory)
52B11 \(n\)-dimensional polytopes
60C05 Combinatorial probability
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