Binary Linear Codes, Dimers and Hypermatrices

We show that the weight enumerator of any binary linear code is equal to the permanent of a 3-dimensional hypermatrix (3-matrix). We also show that each permanent is a determinant of a 3-matrix. As an application we write the dimer partition function of a finite 3-dimensional cubic lattice as the de...

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Bibliographic Details
Main Authors Loebl, Martin, Rytíř, Pavel
Format Journal Article
LanguageEnglish
Published 07.02.2013
Subjects
Mathematics - Combinatorics
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Summary:We show that the weight enumerator of any binary linear code is equal to the permanent of a 3-dimensional hypermatrix (3-matrix). We also show that each permanent is a determinant of a 3-matrix. As an application we write the dimer partition function of a finite 3-dimensional cubic lattice as the determinant of the vertex-adjacency 3-matrix of a 2-dimensional simplicial complex which preserves the natural embedding of the cubic lattice.
DOI:10.48550/arxiv.1302.1722