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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
https://izlik.org/JA79YK38SW

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
https://izlik.org/JA79YK38SW

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
Authors

Fikri Gökpınar

Publication Date March 28, 2010
IZ https://izlik.org/JA79YK38SW
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. https://izlik.org/JA79YK38SW
AMA 1.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):127-132. https://izlik.org/JA79YK38SW
Chicago Gökpınar, Fikri. 2010. “A Simulation Study on Decoding of Binary Linear Codes Using Projective Geometry PG(3,2)”. Gazi University Journal of Science 20 (4): 127-32. https://izlik.org/JA79YK38SW.
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 [1]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, Mar. 2010, [Online]. Available: https://izlik.org/JA79YK38SW
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 1, 2010): 127-132. https://izlik.org/JA79YK38SW.
JAMA 1.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, Mar. 2010, pp. 127-32, https://izlik.org/JA79YK38SW.
Vancouver 1.Gökpınar F. A Simulation Study on Decoding of Binary Linear Codes Using Projective Geometry PG(3,2). Gazi University Journal of Science [Internet]. 2010 Mar. 1;20(4):127-32. Available from: https://izlik.org/JA79YK38SW