Even lattices and doubly even codes
type: Item
instance of: scholarly article
title: Even lattices and doubly even codes
zbMATH Open document ID: 0726.94009
author: Masaaki Kitazume
author: Takeshi Kondo
author: Izumi Miyamoto
published in: Journal of the Mathematical Society of Japan
publication date: 1991-01-01T00:00:00Z
review text: In this paper, we study three methods to construct even lattices in an n- dimensional Euclidean space \(E^ n\) from doubly even codes of length n. The first two methods are the constructions A, B appeared in Conway- Sloane's book ``Sphere packings, lattices and groups'', and the third method is a generalization of the construction of the Leech lattice from the Golay code. We prove that non-equivalent codes yield non-equivalent lattices except some small dimension cases. Some counter examples are given. We consider the structure of the code, and construct some automorphisms of the lattice. Our main results follow from the transitivity of the automorphism group on some family of orthogonal bases of the Euclidean space \(E^ n\).
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 51M05
zbMATH DE Number: 4200137
zbMATH Keywords: even lattices
zbMATH Keywords: doubly even codes
zbMATH Keywords: Leech lattice
zbMATH Keywords: Golay code
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04310067
OpenAlex ID: W2056558225
DOI: 10.2969/JMSJ/04310067
description: scientific article; zbMATH DE number 4200137