Binary linear codes via 4D discrete Ihara–Selberg function

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 1960s for the special case of the Ising partition functi...

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Veröffentlicht in:	Annales de l'Institut Henri Poincaré. D. Combinatorics, physics and their interactions physics and their interactions, 2019-01, Vol.6 (1), p.73-95
1. Verfasser:	Loebl, Martin
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Statistical mechanics, structure of matter
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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 1960s for the special case of the Ising partition function of the 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 the cubic 3D lattices.
ISSN:	2308-5827 2308-5835
DOI:	10.4171/AIHPD/65