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Construction of the Best Binary Cyclic Codes of Even Length

  • J.-P. Martin
Part of the International Centre for Mechanical Sciences book series (CISM, volume 339)

Abstract

This paper gives a method of construction for binary cyclic codes of even length out of shorter ones of odd length. This construction enables us to establish the set of the minimal distances reached by even length codes, and for each of these distances, to determine the associated generator polynomial of lowest degree. Thanks to this result we construct the complete table of the best possible binary cyclic codes on each minimal distance up to the length 64, finishing off in that way the table of the binary cyclic codes of odd length compiled by CHEN and lying in [5]. It can be noticed that VAN LINT found similar results but for only few specific values, see [3].

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References

  1. [1]
    F.J. Macwilliams and N.J.A. Sloane, The theory of error-correcting codes, Amsterdam, North-Holland, 1977.zbMATHGoogle Scholar
  2. [2]
    G. Castagnoli, J.L. Massey, P.A. Schoeller and N. Von Seemann, “On repeated-root cyclic codes”, IEEE Trans. Inform. Theory, vol. 37, no. 2, pp. 337–342, Mar.1991.CrossRefzbMATHMathSciNetGoogle Scholar
  3. [3]
    J.H. Van Lint, “Repeated-root cyclic codes”, IEEE Trans. Inform. Theory, vol. 37, no. 2, pp. 343–345, Mar.1991.CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    H. Hasse, “Theorie der höheren Differentiale in einem algebraischen Funktionenkörper mit vollkommenem Konstantenkörper hei beliebiger Charakteristik”, J. Reine. Ang. Math., vol. 175, pp. 50–54, 1936.Google Scholar
  5. [5]
    W.W. Peterson and E.J. Weldon, Jr, Error-Correcting Codes, Second ed. Cambridge, MA: MIT Press, 1972.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • J.-P. Martin
    • 1
  1. 1.G.E.C.T.University of Toulon and VarLa GardeFrance

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