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ISRN Algebra
Volume 2012 (2012), Article ID 956017, 14 pages
http://dx.doi.org/10.5402/2012/956017
Research Article

Codes over Graphs Derived from Quotient Rings of the Quaternion Orders

1Departamento de Matemática, ICEx, UNIFAL, R. Gabriel Monteiro da Silva, 700 Centro, 37130-000 Alfenas, MG, Brazil
2Departamento de Telemática, FEEC, UNICAMP, Avenida Albert Einstein 400, Cidade Universtaria Zeferino Vaz, 13083-852 Campinas, SP, Brazil

Received 13 February 2012; Accepted 6 March 2012

Academic Editors: H. Airault, A. Milas, and H. You

Copyright © 2012 Cátia R. de O. Quilles Queiroz and Reginaldo Palazzo Júnior. 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.

Abstract

We propose the construction of signal space codes over the quaternion orders from a graph associated with the arithmetic Fuchsian group Γ 8 . This Fuchsian group consists of the edge-pairing isometries of the regular hyperbolic polygon (fundamental region) P8, which tessellates the hyperbolic plane 𝔻 2 . Knowing the generators of the quaternion orders which realize the edge pairings of the polygon, the signal points of the signal constellation (geometrically uniform code) derived from the graph associated with the quotient ring of the quaternion order are determined.