Hierarchical Models, Marginal Polytopes, and Linear Codes

TL;DR

This paper investigates the relationship between binary hierarchical models, their associated marginal polytopes, and the convex hulls of linear codes, providing classifications and algorithms for these structures.

Contribution

It characterizes which linear codes can be realized by hierarchical models and offers an algorithm to identify such polytopes.

Findings

Classified all full-dimensional polytopes with vertices forming linear codes.

Determined the class of linear codes realizable by hierarchical models.

Provided an algorithm to identify these polytopes.

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.