标题： 分层模型，边缘多面体和线性码 显示英文标题

标题： Hierarchical Models, Marginal Polytopes, and Linear Codes

摘要： 在本文中，我们探讨二进制分层模型、其边缘多面体和码字多面体之间的联系，即线性码的凸包。 确定了可通过分层模型实现的线性码类别。 我们对所有具有顶点形成线性码性质的全维多面体进行了分类，并给出一个确定它们的算法。 显示英文摘要

摘要： 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.