Geodesic
Hierarchical models, marginal polytopes, and linear codes
Kybernetika, Tome 45 (2009) no. 2, pp. 189-207

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In this paper, 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.
Classification : 52B11, 60C05, 94B05
Keywords: 0/1 polytopes; linear codes; hierarchical models; exponential families 
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     title = {Hierarchical models, marginal polytopes, and linear codes},
     journal = {Kybernetika},
     pages = {189--207},
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     zbl = {1167.94340},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009__45_2_a1/}
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Kahle, Thomas; Wenzel, Walter; Ay, Nihat. Hierarchical models, marginal polytopes, and linear codes. Kybernetika, Tome 45 (2009) no. 2, pp. 189-207. http://geodesic.mathdoc.fr/item/KYB_2009__45_2_a1/