

Preprint 30/2008
Hierarchical Models, Marginal Polytopes, and Linear Codes
Thomas Kahle, Walter Wenzel, and Nihat Ay
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Submission date: 01. Apr. 2008 (revised version: November 2008)
Pages: 20
published in: Kybernetika, 45 (2009) 2, p. 189-207
Bibtex
MSC-Numbers: 52B11, 94B05, 60C05
Keywords and phrases: 0/1 polytopes, linear codes, hierarchical models, exponential families
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Abstract:
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.