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On the density of best coverings in hamming spaces

  • Coding And Combinatorics
  • Conference paper
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Coding Theory and Applications (Coding Theory 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 311))

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Nous présentons des constructions pour des recouvrements d'espaces de Hamming binaires de dimension n par des sphères de rayon 1. Nous montrons que la densité minimale μn de tels recouvrements est au plus 3/2. Le comportement asymptotique de μn quand n tend vers l'infini n'est pas connu.

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References

  1. G.D. COHEN, M.G. KARPOVSKY, H.F. MATTSON, Jr. and J.R. SCHATZ: "Covering radius-survey and recent results", IEEE Trans. Inform. Theory, vol. IT-31, pp. 328–343, 1985.

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  2. G.L. KATSMAN and S.N. LITSYN: Private Communication.

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  3. M. MOLLARD: "A generalized parity function and its use in the construction of perfect codes", SIAM J.Alg. Disc. Math., vol 7. no 1, 113–115, 1986.

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  4. A. LOBSTEIN, G.D. COHEN and N.J.A. SLOANE: "Recouvrements d'espaces de Hamming Binaires", C.R. Acad. Sc. Paris, t. 301, Série I, no 5, pp. 135–138, 1985.

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Authors
  1. M. Beveraggi
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  2. G. Cohen
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Editor information

G. Cohen P. Godlewski

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© 1988 Springer-Verlag Berlin Heidelberg

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Beveraggi, M., Cohen, G. (1988). On the density of best coverings in hamming spaces. In: Cohen, G., Godlewski, P. (eds) Coding Theory and Applications. Coding Theory 1986. Lecture Notes in Computer Science, vol 311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19368-5_4

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  • DOI: https://doi.org/10.1007/3-540-19368-5_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19368-5

  • Online ISBN: 978-3-540-39243-9

  • eBook Packages: Springer Book Archive

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