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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.

Linked References

  1. A. F. Beardon, The Geometry of Discrete Groups, vol. 91 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. G. D. Forney Jr., “Geometrically uniform codes,” Institute of Electrical and Electronics Engineers, vol. 37, no. 5, pp. 1241–1260, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. H. Lazari and R. Palazzo Jr., “Geometrically uniform hyperbolic codes,” Computational & Applied Mathematics, vol. 24, no. 2, pp. 173–192, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. S. I. R. Costa, M. Muniz, E. Agustini, and R. Palazzo Jr., “Graphs, tessellations, and perfect codes on flat tori,” Institute of Electrical and Electronics Engineers, vol. 50, no. 10, pp. 2363–2377, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. C. Martínez, R. Beivide, and E. M. Gabidulin, “Perfect codes from Cayley graphs over Lipschitz integers,” Institute of Electrical and Electronics Engineers, vol. 55, no. 8, pp. 3552–3562, 2009. View at Publisher · View at Google Scholar
  6. C. Quilles and R. Palazzo Jr., “Quasi-perfect geometrically uniform codes derived from graphs over gaussian integer rings,” in Proceedings of the IEEE International Symposium on Information Theory, pp. 1158–1162, Austin, Tex, USA, June 2010.
  7. C. Quilles and R. Palazzo Jr., “Quasi-perfect geometrically uniform codes derived from graphs over integer rings,” in Proceedings of the 3rd International Castle Meeting on Coding Theory and Applications, pp. 239–244, Barcelona, Spain, September 2011.
  8. P. A. Firby and C. F. Gardiner, Surface Topology, Woodhead, 3rd edition, 2001.
  9. O. T. O'Meara, Introduction to Quadratic Forms, Springer, New York, NY, USA, 1973.
  10. T. W. Hungerford, Algebra, vol. 73 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1980.
  11. K. Takeuchi, “A characterization of arithmetic Fuchsian groups,” Journal of the Mathematical Society of Japan, vol. 27, no. 4, pp. 600–612, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. I. Stewart and D. Tall, Algebraic Number Theory, Chapman and Hall Mathematics Series, Chapman & Hall, London, UK, 2nd edition, 1987.
  13. V. L. Vieira, Arithmetic fuchsian groups identified over the quaternion orders for the construction of signal constellations [Doctoral Dissertation], FEEC-UNICAMP, 2007.
  14. I. Reiner, Maximal Orders, vol. 28 of London Mathematical Society Monographs. New Series, The Clarendon Press Oxford University Press, Oxford, UK, 2003.
  15. S. Johansson, A description of quaternion algebra, http://www.math.chalmers.se/~sj/forskning.html.
  16. S. Katok, Fuchsian Groups, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, Ill, USA, 1992.
  17. E. D. Carvalho, Construction and labeling of geometrically uniform signal constellations in euclidean and hyperbolic spaces [Doctoral Dissertation], FEEC-UNICAMP, 2001.