Lattices with theta functions for G(\(\sqrt{2})\) and linear codes
type: Item
instance of: scholarly article
title: Lattices with theta functions for G(\(\sqrt{2})\) and linear codes
zbMATH Open document ID: 0609.10026
DOI: 10.1016/0021-8693(87)90208-0
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: The author uses codes over the fields with 2 and 9 elements to construct unimodular complex lattices over \({\mathbb{Z}}[e^{\pi i/4}]\) with large minimum norm. The methods are extensions of work by \textit{N. J. A. Sloane} [ibid. 52, 168-181 (1978; Zbl 0376.94009)] who treated lattices over \({\mathbb{Z}}[e^{2\pi i/3}]\). Several lattices constructed are extremal with respect to a bound on the minimum norm obtained through modular forms.
Mathematics Subject Classification ID: 11H31
Mathematics Subject Classification ID: 11F99
Mathematics Subject Classification ID: 94B99
Mathematics Subject Classification ID: 11H06
zbMATH DE Number: 3985328
zbMATH Keywords: extremal theta-function
zbMATH Keywords: sphere-packings
zbMATH Keywords: codes
zbMATH Keywords: unimodular complex lattices
zbMATH Keywords: large minimum norm
zbMATH Keywords: modular forms
author: Heinz-Georg Quebbemann
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90208-0
OpenAlex ID: W1982272927
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description: scientific article; zbMATH DE number 3985328