Abstract
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).
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
F. J. MacWilliams, “Permutation Decoding of Systematic Codes,” Bell Syst. Tech. J., vol. 43, pp. 485–505, 1964
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.
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.
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.
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.
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.
W. W. Peterson, Error-Correcting Codes, The MIT Press, 1972.
F. J. MacWillians and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977.
Vera Pless, Introduction to the Theory of Error-Correcting Codes, John Willey and Sons, New York, 1982.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Le-Ngoc, T., Jia, M., Benyamin-Seeyar, A. (1994). Permutation decoding using primitive elements as multipliers. In: Gulliver, T.A., Secord, N.P. (eds) Information Theory and Applications. ITA 1993. Lecture Notes in Computer Science, vol 793. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57936-2_45
Download citation
DOI: https://doi.org/10.1007/3-540-57936-2_45
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57936-6
Online ISBN: 978-3-540-48392-2
eBook Packages: Springer Book Archive