Binary Linear Codes, Dimers and Hypermatrices
Combinatorics
2016-09-28 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1302.1722,
title = {Binary Linear Codes, Dimers and Hypermatrices},
author = {Martin Loebl and Pavel Rytíř},
journal= {arXiv preprint arXiv:1302.1722},
year = {2016}
}
Comments
To appear in the proceedings of 10th Random Generation of Combinatorial Structures (GASCom) (2016). 10 pages, 6 figures