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Journal of Discrete Mathematics
Volume 2013 (2013), Article ID 625912, 5 pages
http://dx.doi.org/10.1155/2013/625912
Research Article

On Maximum Lee Distance Codes

Department of Mathematical Sciences, University of New Brunswick Saint John, Saint John, NB, Canada E2L 4L5

Received 25 September 2012; Accepted 21 November 2012

Academic Editor: Annalisa de Bonis

Copyright © 2013 Tim L. Alderson and Svenja Huntemann. 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. C. Y. Lee, “Some properties of nonbinary error-correcting codes,” IEEE Transactions on Information Theory, vol. 4, no. 2, Article ID 012263, pp. 77–82, 1958. View at Publisher · View at Google Scholar
  2. K. Nakamura, “A class of error correcting codes for DPSK channels,” in Proceedings of the International Conference on Communications (ICC '79), vol. 3, p. 45, 1979.
  3. R. M. Roth and P. H. Siegel, “Lee-metric BCH codes and their application to constrained and partial-response channels,” IEEE Transactions on Information Theory, vol. 40, no. 4, pp. 1083–1096, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. M. Blaum, J. Bruck, and A. Vardy, “Interleaving schemes for multidimensional cluster errors,” IEEE Transactions on Information Theory, vol. 44, no. 2, pp. 730–743, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. K.-U. Schmidt, “Complementary sets, generalized Reed-Muller codes, and power control for OFDM,” IEEE Transactions on Information Theory, vol. 53, no. 2, pp. 808–814, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. T. Etzion and E. Yaakobi, “Error-correction of multidimensional bursts,” IEEE Transactions on Information Theory, vol. 55, no. 3, pp. 961–976, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Barg and A. Mazumdar, “Codes in permutations and error correction for rank modulation,” IEEE Transactions on Information Theory, vol. 56, no. 7, pp. 3158–3165, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. J. W. P. Hirschfeld, G. Korchmaros, and F. Torres, Algebraic Curves over a Finite Field, Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ, USA, 2008.
  9. T. L. Alderson, A. A. Bruen, and R. Silverman, “Maximum distance separable codes and arcs in projective spaces,” Journal of Combinatorial Theory A, vol. 114, no. 6, pp. 1101–1117, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. S. Ball, “On sets of vectors of a finite vector space in which every subset of basis size is a basis,” Journal of the European Mathematical Society, vol. 14, no. 3, pp. 733–748, 2012. View at Zentralblatt MATH
  11. K. Shiromoto, “Singleton bounds for codes over finite rings,” Journal of Algebraic Combinatorics, vol. 12, no. 1, pp. 95–99, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. S. T. Dougherty and C. Fernandez-Cordoba, “Codes over 2κ, Gray map and self-dual codes,” Advances in Mathematics of Communications, vol. 5, no. 4, pp. 571–588, 2011. View at Publisher · View at Google Scholar
  13. S. T. Dougherty and K. Shiromoto, “Maximum distance codes over rings of order 4,” IEEE Transactions on Information Theory, vol. 47, no. 1, pp. 400–404, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. I, vol. 16 of North-Holland Mathematical Library, North-Holland Publishing, Amsterdam, The Netherland, 1977.
  15. A. D. Wyner and R. L. Graham, “An upper bound on minimum distance for a k-ary code,” Information and Control, vol. 13, no. 1, pp. 46–52, 1968. View at Zentralblatt MATH · View at Scopus
  16. J. C. Chiang and J. K. Wolf, “On channels and codes for the Lee metric,” Information and Control, vol. 19, no. 2, pp. 159–173, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus