ERROR CORRECTION IN LINEAR CODES WITH COMPUTER

Yıl 2008, Sayı: 016, 39 - 48, 15.09.2008

Aydın Seçer Ayten Özkan Mustafa Bayram

Öz

Within the context of this study, we have improved a computer program on the syndrome decoding method for correcting codewords received incorrect. This program generates code from given generator matrix and calculates the hamming distance which appertains to this code, also, it finds Slepian(1960) standart array. It gives a list of the decoding table of code and an error pattern relating to be received incorrect codewords. We have used Maple Computer Algebra for calculations [5]. The Algorithm, we have given, reproduces different results from given generator matrix. In here, we have chosen a test problem whose code word’s lengthy is 4. But, it is possible for algorithm that it can make calculations for longer codes.

Anahtar Kelimeler

Linear Code, Sydrome Decoding, Coset, Coset Leader, MAPLE

Kaynakça

• [1]Bose R. C., Ray-Chaudhuri D. K., 1960, On a class of error-correcting binary group codes, Info and Control 3, 68-79.
• [2]Hill R., 1986, A first course in coding theory, Clarendon Press, Oxford.
• [3]Huffman W. C. and Pless V., 2003, Fundamentals of Error Correcting Codes, Cambridge University Press.
• [4]Hamming R. W., 1950, Error detecting and error-correcting codes. Bell Syst. T.J. 29, 147-60.
• [5]Monagan M. B., Geddes K. O., Heal K. M., Labahn G., Vorkoetter S. M., McCarron J. and DeMarco P., 2003, Maple 9 Advanced Programming Guide. Maplesoft, a division of Waterloo Maple Inc.
• [6]Shannon C. E., 1948, A mathematical theory of communication. Bell Syst. T.J. 27, 379-423.
• [7]Slepian D., 1960, Some further theory of group codes. Bell Syst. Tech.J. 39, 1219-52.