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

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1988)

Part of the book series: Lecture Notes in Computer Science ((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. BERLEKAMP, E.R.,MORENO, O., "Extended double-error correcting binary GOPPA codes are cyclic" IEEE Trans.Info.Theory 19 (1973),817–818.

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  2. LACHAUD,G.,WOLFMANN,J., "Sommes de Kloosterman,courbes elliptiques et codes cycliques en caracteristique 2" C.R.Acad.Sci.Paris (1),305 (1987)

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  3. McWILLIAMS, F.J.,SLOANE, N.J.A., "The theory of Error-correcting codes" North-Holland, Amsterdam, 1977.

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  4. TZENG, K.K.,ZIMMERMANN, K., "On extending GOPPA codes to cyclic codes" IEEE Trans.Info.Theory 21 (1975),712–716.

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Authors and Affiliations

  1. G.E.C.T, Université de Toulon, 83130, La Garde, France

    J. Wolfmann

Authors
  1. J. Wolfmann
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Teo Mora

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© 1989 Springer-Verlag Berlin Heidelberg

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Wolfmann, J. (1989). The weights of the orthogonals of certain cyclic codes or extended GOPPA codes. In: Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1988. Lecture Notes in Computer Science, vol 357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51083-4_84

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  • DOI: https://doi.org/10.1007/3-540-51083-4_84

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51083-3

  • Online ISBN: 978-3-540-46152-4

  • eBook Packages: Springer Book Archive

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