Permutation decoding using primitive elements as multipliers

  • Tho Le-Ngoc
  • Ming Jia
  • Anader Benyamin-Seeyar
Decoding Techniques
Part of the Lecture Notes in Computer Science book series (LNCS, volume 793)


Permutation decoding employs a very simple combinational logic circuit for error detection and correction. In this paper, the topic of permutation decoding using primitive elements of a prime field as multipliers is addressed in order to increase the capability of the well known (T, U) permutation decoding method in decoding cyclic codes of prime length. Since only error positions are involved in the analysis, the results are applicable to cyclic codes over GF(2q).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    F. J. MacWilliams, “Permutation Decoding of Systematic Codes,” Bell Syst. Tech. J., vol. 43, pp. 485–505, 1964Google Scholar
  2. [2]
    A. Benyamin-Seeyar, S. S. Shiva, and V. K. Bhargava, “Capability of the Error-Trapping Cyclic Code,” IEEE Trans. Inform. Theory, vol. 32, No. 2, pp. 166–180, Mar. 1986.Google Scholar
  3. [3]
    M. Jia, A. Benyamin-Seeyar, and T. Le-Ngoc, “Exact Lower Bounds on the Code Length of Three-Step Permutation-Decodable Cyclic Codes,” 1991 IEEE International Symposium on Information Theory, Budapest, Hungary.Google Scholar
  4. [4]
    M. Jia, A. Benyamin-Seeyar, and T. Le-Ngoc, “On the Capability of (T, U) Permutation Decoding Method,” 1991 Canadian Conference on Electrical And Computer Engineering, Quebec, Canada.Google Scholar
  5. [5]
    S. G. S. Shiva and K. C. Fung, “Permutation Decoding of Certain Triple-Error-Correcting Binary Codes,” IEEE Trans. Inf. Theory, IT-8, pp 444–446, May 1972.Google Scholar
  6. [6]
    P. W. Yip, S. G. S. Shiva and E. L. Cohen, “Permutation Decodable Binary Cyclic Codes,” Electronic Letters, Vol. 10, pp. 467–468, October 1974.Google Scholar
  7. [7]
    W. W. Peterson, Error-Correcting Codes, The MIT Press, 1972.Google Scholar
  8. [8]
    F. J. MacWillians and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977.Google Scholar
  9. [9]
    Vera Pless, Introduction to the Theory of Error-Correcting Codes, John Willey and Sons, New York, 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Tho Le-Ngoc
    • 1
  • Ming Jia
    • 1
  • Anader Benyamin-Seeyar
    • 1
  1. 1.Department of Electrical and Computer EngineeringConcordia UniversityMontrealCanada

Personalised recommendations