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The equivalence classes of the Vasil'ev codes of length 15

Part of the Lecture Notes in Mathematics book series (LNM,volume 969)

Abstract

In this paper we determine the equivalence classes of the perfect Vasilev codes of length 15: There exist 19 non equivalent Vasil'ev codes (including the Hamming code). If we restrict the equivalence transformations to permutations of coordinates we get 64 different Vasil'ev codes.

Keywords

  • Equivalence Class
  • Normal Form
  • Binary Code
  • Linear Code
  • Equivalence Transformation

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References

  1. H.Bauer, B.Ganter, F.Hergert: Algebraic techniques for nonlinear codes. TH Darmstadt, Preprint-Nr. 609 (1981).

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  2. F.Hergert: Beiträge zur Theorie nichtlinearer Fehler-korrigierender Codes. Diplomarbeit TH Darmstadt (1980) (unpublished).

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  3. F.J.MacWilliams, N.J.A.Sloane: The theory of error-correcting codes. North-Holland Publ. Comp. (1978).

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  4. J.L.Vasil'ev: On nongroup close-packed codes. Probl.Kibernet., 8 (1962).

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© 1982 Springer-Verlag

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Hergert, F. (1982). The equivalence classes of the Vasil'ev codes of length 15. In: Jungnickel, D., Vedder, K. (eds) Combinatorial Theory. Lecture Notes in Mathematics, vol 969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062993

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  • DOI: https://doi.org/10.1007/BFb0062993

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11971-5

  • Online ISBN: 978-3-540-39380-1

  • eBook Packages: Springer Book Archive