International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 15, Pages 935-946

On the structure of multipliers of 2

Edgar Martínez-Moro1 and Roberto Canogar-Mckenzie2

1Departamento de Matemática Aplicada Fundamental, Universidad de Valladolid, Valladolid, Spain
2Departamento de Matemáticas, Universidad Nacional deEducación a Distancia (UNED), Madrid, Spain

Received 14 March 2002

Copyright © 2003 Edgar Martínez-Moro and Roberto Canogar-Mckenzie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We show the combinatorial structure of 2 modulo sublattices similar to 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 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 the coding theory.