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Journal of Electronics (China)

, Volume 1, Issue 1, pp 12–17 | Cite as

An algebraic complete decoding for double-error-correcting binary BCH codes

  • Feng Gulliang
Article
  • 41 Downloads

Abstract

An algebraic complete decoding for double-error-correcting binary BCH codes of primitive length is derived. The decoding is done more quickly than the step-by-step decoding devised by Hartmann. And if an error pattern corresponding with syndromess 1 ands 2 has weight 3, the decoding can find all error patterns of weight 3 corresponding with these syndromes. At the same time, a discriminant for a polynomial of degree 3 overGF(2 m ) has three distinct roots inGF2 m ) is also derived. The discriminant is very important for complete decoding of triple-error-correcting binary BCH codes.

Keywords

Conjugate Class Minimum Polynomial Error Pattern Primitive Element Distinct Root 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    D. C. Govenstein, W. W. Peterson and N. Zierler,Inform. Contr. 3 (1960), 291.CrossRefGoogle Scholar
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    F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, New York, 1977, p. 279.MATHGoogle Scholar
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    C. R. P. Hartmann,IEEE Trans. on IT,IT-17 (1971), 765.MATHCrossRefGoogle Scholar
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    J. A. V. D. Horst and T. Berger,IEEE Trans. on IT,IT-22 (1976), 138.MATHCrossRefGoogle Scholar
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    E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, New York, 1968.MATHGoogle Scholar

Copyright information

© Science Press 1984

Authors and Affiliations

  • Feng Gulliang
    • 1
  1. 1.Shanghai Institute of Computer TechnologyShanghaiChina

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