On the structure of multipliers of \(\mathbb{Z}^2\)
type: Item
instance of: scholarly article
title: On the structure of multipliers of \(\mathbb{Z}^2\)
zbMATH Open document ID: 1012.05157
DOI: 10.1155/S0161171203203124
author: E. Martínez-Moro
author: Roberto Canogar-Mckenzie
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-03-17T00:00:00Z
full work available at URL: https://eudml.org/doc/50007
review text: Summary: We show the combinatorial structure of \(\mathbb{Z}^2\) modulo sublattices similar to \(\mathbb{Z}^2\). The tool we use for dealing with this purpose is the notion of association scheme. We classify when the scheme defined by the lattice is imprimitive and characterize its decomposition in terms of the decomposition of the Gaussian integer defining the lattice. This arises in the classification of different forms of tiling \(\mathbb{Z}^{2}\) by lattices of this type. The main application of these structures is that they are closely related to two-dimensional signal constellations with a Mannheim metric in coding theory.
Mathematics Subject Classification ID: 05E20
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 11Z05
zbMATH DE Number: 1883719
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1883719