Binary linear codes via 4D discrete Ihara-Selberg function
Combinatorics
2016-09-20 v3
Abstract
We express the weight enumerator of each binary linear code, in particular the Ising partition function of an arbitrary finite graph, as a formal infinite product. An analogous result was obtained by Feynman and Sherman in the beginning of the 1960's for the special case of the Ising partition function of planar graphs. A product expression is an important step towards understanding the logarithm of the Ising partition function, for general graphs and in particular for cubic 3D lattices.
Cite
@article{arxiv.1503.02525,
title = {Binary linear codes via 4D discrete Ihara-Selberg function},
author = {Martin Loebl},
journal= {arXiv preprint arXiv:1503.02525},
year = {2016}
}
Comments
The third version contains several small updates suggested by reviewers