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

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.

 

Keywords

• Key Words: Projective geometry, Binary linear codes, Error-correcting codes, Decoding

References

1. Cameron, P. J., “Combinatorics: Topics,
2. Techniques, Algorithms”, Cambridge University Press, (1996).
3. Assmus, E. F., Key, J. D., “Hadamard Matrices And Their Design”, Transactions of the American Mathematical Society, 330: 269-293 (1989).
4. Assmus, E. F., “On the theory of designs, Surveys in Combinatorics”, 141, Cambridge University Press, 1-21 (1989).
5. 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).
6. Xambo- Descamps, S., “Block error-Correcting Codes: A computational premier”, Springer- Verlag, New York, 112-114 (2003).
7. Garret, P., “The Mathematics of coding theory”, Prentice Hall, New York (2004).
8. Wicker, S. B, Kim, S., “Fundementals of codes, graphs and iterative decoding”, Kluvwer Academic Publishers, London, 78-80 (2003).

9. Beutelspacher, A., Rosenbaum, U., “Projective Geometry”. Cambridge University Press, London, 25-30 (1998).
10. Raghavarao, D., “Constructions and Combinatorial Problems in Design of Experiments”, Dover, New York, 56-57 (1971).