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A Simulation Study on Decoding of Binary Linear Codes Using Projective Geometry PG(3,2)

Year 2007, Volume: 20 Issue: 4, 127 - 132, 28.03.2010

Abstract

Projective geometry is used to decode and represent codes easily. Cameron [1] generated a binary linear code from PG(2,2). In this paper we construct a binary linear code from PG(3,2). Also we give a decoding rule for this code. A simulation study is given to compare this decoding algorithm with maximum likelihood decoding algorithm.

 

References

  • Cameron, P. J., “Combinatorics: Topics,
  • Techniques, Algorithms”, Cambridge University Press, (1996).
  • Assmus, E. F., Key, J. D., “Hadamard Matrices And Their Design”, Transactions of the American Mathematical Society, 330: 269-293 (1989).
  • Assmus, E. F., “On the theory of designs, Surveys in Combinatorics”, 141, Cambridge University Press, 1-21 (1989).
  • Assmus, E. F., “The coding theory of finite geometries and designs”, Lecture Notes in Computer Science, Edited by T. Mora, Springer- Verlag, 357: 1-6 (1998).
  • Xambo- Descamps, S., “Block error-Correcting Codes: A computational premier”, Springer- Verlag, New York, 112-114 (2003).
  • Garret, P., “The Mathematics of coding theory”, Prentice Hall, New York (2004).
  • Wicker, S. B, Kim, S., “Fundementals of codes, graphs and iterative decoding”, Kluvwer Academic Publishers, London, 78-80 (2003).
  • Beutelspacher, A., Rosenbaum, U., “Projective Geometry”. Cambridge University Press, London, 25-30 (1998).
  • Raghavarao, D., “Constructions and Combinatorial Problems in Design of Experiments”, Dover, New York, 56-57 (1971).
Year 2007, Volume: 20 Issue: 4, 127 - 132, 28.03.2010

Abstract

References

  • Cameron, P. J., “Combinatorics: Topics,
  • Techniques, Algorithms”, Cambridge University Press, (1996).
  • Assmus, E. F., Key, J. D., “Hadamard Matrices And Their Design”, Transactions of the American Mathematical Society, 330: 269-293 (1989).
  • Assmus, E. F., “On the theory of designs, Surveys in Combinatorics”, 141, Cambridge University Press, 1-21 (1989).
  • Assmus, E. F., “The coding theory of finite geometries and designs”, Lecture Notes in Computer Science, Edited by T. Mora, Springer- Verlag, 357: 1-6 (1998).
  • Xambo- Descamps, S., “Block error-Correcting Codes: A computational premier”, Springer- Verlag, New York, 112-114 (2003).
  • Garret, P., “The Mathematics of coding theory”, Prentice Hall, New York (2004).
  • Wicker, S. B, Kim, S., “Fundementals of codes, graphs and iterative decoding”, Kluvwer Academic Publishers, London, 78-80 (2003).
  • Beutelspacher, A., Rosenbaum, U., “Projective Geometry”. Cambridge University Press, London, 25-30 (1998).
  • Raghavarao, D., “Constructions and Combinatorial Problems in Design of Experiments”, Dover, New York, 56-57 (1971).
There are 10 citations in total.

Details

Primary Language English
Journal Section Statistics
Authors

Fikri Gökpınar

Publication Date March 28, 2010
Published in Issue Year 2007 Volume: 20 Issue: 4

Cite

APA Gökpınar, F. (2010). A Simulation Study on Decoding of Binary Linear Codes Using Projective Geometry PG(3,2). Gazi University Journal of Science, 20(4), 127-132.
AMA Gökpınar F. A Simulation Study on Decoding of Binary Linear Codes Using Projective Geometry PG(3,2). Gazi University Journal of Science. March 2010;20(4):127-132.
Chicago Gökpınar, Fikri. “A Simulation Study on Decoding of Binary Linear Codes Using Projective Geometry PG(3,2)”. Gazi University Journal of Science 20, no. 4 (March 2010): 127-32.
EndNote Gökpınar F (March 1, 2010) A Simulation Study on Decoding of Binary Linear Codes Using Projective Geometry PG(3,2). Gazi University Journal of Science 20 4 127–132.
IEEE F. Gökpınar, “A Simulation Study on Decoding of Binary Linear Codes Using Projective Geometry PG(3,2)”, Gazi University Journal of Science, vol. 20, no. 4, pp. 127–132, 2010.
ISNAD Gökpınar, Fikri. “A Simulation Study on Decoding of Binary Linear Codes Using Projective Geometry PG(3,2)”. Gazi University Journal of Science 20/4 (March 2010), 127-132.
JAMA Gökpınar F. A Simulation Study on Decoding of Binary Linear Codes Using Projective Geometry PG(3,2). Gazi University Journal of Science. 2010;20:127–132.
MLA Gökpınar, Fikri. “A Simulation Study on Decoding of Binary Linear Codes Using Projective Geometry PG(3,2)”. Gazi University Journal of Science, vol. 20, no. 4, 2010, pp. 127-32.
Vancouver Gökpınar F. A Simulation Study on Decoding of Binary Linear Codes Using Projective Geometry PG(3,2). Gazi University Journal of Science. 2010;20(4):127-32.