Weight distribution of translates of MDS codes

Abstract

The following is a particular case of a theorem of Delsarte: the weight distribution of a translate of an MDS code is uniquely determined by its firstn−k terms. Here an explicit formula is derived from a completely different approach.

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References

  1. [1]

    E. R. Berlekamp,Algebraic Coding Theory, McGraw-Hill, New York (1968).

    Google Scholar 

  2. [2]

    P. G. Bonneau, Un Renforcement de la Formule d'Enumération des Poids des codes optimaux,C. R. Acad. Sc. Paris, t. 296 Série I (1983), 863, 4.

    Google Scholar 

  3. [3]

    P. G. Bonneau,Codes et Combinatoire (thesis), Université Pierre et Marie Curie, Paris (1984).

    Google Scholar 

  4. [4]

    L. Comtet,Analyse Combinatoire (tome second) Presses Universitaires de France, Paris (1970).

    Google Scholar 

  5. [5]

    Ph. Delsarte, Four Fondamental Parameters of a Code and Their Combinatorial Significance,Info. and Control,23 (1973), 407–438.

    Google Scholar 

  6. [6]

    J. Denes andA. D. Keedwell,Latin Squares and their Applications, Academic Press, New York (1974).

    Google Scholar 

  7. [7]

    W. Heise andP. Quattrocchi,Informations- und Codierungstheorie, Springer-Verlag, Berlin, Heidelberg New York (1983).

    Google Scholar 

  8. [8]

    A. Marguinaud, Codes a Distance Maximale,Revue du Cethedec,22 (1970), 33–46.

    Google Scholar 

  9. [9]

    F. J. Mac Williams andN. J. A. Sloane,The Theory of Error-Correcting codes (third printing), North Holland-Amsterdam, New York, Oxford (1981).

    Google Scholar 

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Bonneau, P.G. Weight distribution of translates of MDS codes. Combinatorica 10, 103–105 (1990). https://doi.org/10.1007/BF02122700

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AMS subject classification (1980)

  • 94B60