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The weights of the orthogonals of certain cyclic codes or extended GOPPA codes

  • J. Wolfmann
Extended Abstracts
Part of the Lecture Notes in Computer Science book series (LNCS, volume 357)

Abstract

Starting from results on elliptic curves and Kloosterman sums over the finite field GF(2t), we determine the weights of the orthogonals of the following binary linear codes : the Melas code of length 2t−1, the irreducible cyclic binary code of length 2t+1, and the extended binary Goppa codes defined by polynomials of degree two.

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References

  1. [1]
    BERLEKAMP, E.R.,MORENO, O., "Extended double-error correcting binary GOPPA codes are cyclic" IEEE Trans.Info.Theory 19 (1973),817–818.Google Scholar
  2. [2]
    LACHAUD,G.,WOLFMANN,J., "Sommes de Kloosterman,courbes elliptiques et codes cycliques en caracteristique 2" C.R.Acad.Sci.Paris (1),305 (1987)Google Scholar
  3. [3]
    McWILLIAMS, F.J.,SLOANE, N.J.A., "The theory of Error-correcting codes" North-Holland, Amsterdam, 1977.Google Scholar
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    TZENG, K.K.,ZIMMERMANN, K., "On extending GOPPA codes to cyclic codes" IEEE Trans.Info.Theory 21 (1975),712–716.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • J. Wolfmann
    • 1
  1. 1.G.E.C.TUniversité de ToulonLa GardeFrance

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