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

Yıl 2007, Cilt: 20 Sayı: 4, 127 - 132, 28.03.2010

Fikri Gökpınar

Öz

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.

 

Anahtar Kelimeler

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

Kaynakça

• 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).