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Relation between the minimum weight of a linear code over GF(qm) and its q-ary image over GF(q)

  • Patrice Rabizzoni
Section III Combinatorial And Algebraic Aspects
Part of the Lecture Notes in Computer Science book series (LNCS, volume 388)

Abstract

In this paper we give an upper bound for the minimum distance of the q-ary image of a linear code over GF(qs). This allows us to give some indications about the minimum distance of the q-ary image of MDS codes over GF(qs) when q=2 and q=3.

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References

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    F.J Macwilliams N.J.A. Sloane, "The theory of error correcting codes", North Holland, Amsterdam, (1977).Google Scholar
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    G. Pasquier, "Etude des codes sur une extension de F2 et de leurs images binaires", Thèse de Doctorat de 3ième cycle, Université de Provence, (1980).Google Scholar
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    G. Pasquier, "The binary Golay obtained from an extended cyclic code over F8", European J. of Combinatorics 1 (1980) 369–370.Google Scholar
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    P. Rabizzoni, "Démultipliés de codes sur une extension de Fq", Thèse de Doctorat de 3ième cycle, Université de Provence, (1983).Google Scholar
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    J. Wolfmann, "A new construction of the binary Golay Code (24, 12, 8) using a group algebra over a finite field", Discrete Math J 1 (1981), 337–338.Google Scholar
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    V. Zinov'ev, Dumer, "Some new maximal codes over F4", Problems of information Transmission (1979).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Patrice Rabizzoni
    • 1
  1. 1.G.E.C.T. U.E.R. de Sciences et TechniquesUniversité de Toulon et du VarGardeFrance

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