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Codes Based on Complete Graphs

In: Designs and Finite Geometries

Author

Listed:
  • Dieter Jungnickel

    (Universität Augsburg, Lehrstuhl für Angewandte Mathematik II)

  • Marialuisa J. De Resmini

    (Università di Roma “La Sapienza”, Dipartimento di Matematica)

  • Scott A. Vanstone

    (University of Waterloo, Dept. of Combinatorics and Optimization)

Abstract

We consider the problem of embedding the even graphical code based on the complete graph on n vertices into a shortening of a Hamming code of length 2 m - 1, where m = h(n) should be as small as possible. As it turns out, this problem is equivalent to the existence problem for optimal codes with minimum distance 5, and optimal embeddings can always be realized as graphical codes based on K n . As a consequence, we are able to determine h(n) exactly for all n of the form 2 k + 1 and to narrow down the possibilities in general to two or three conceivable values.

Suggested Citation

  • Dieter Jungnickel & Marialuisa J. De Resmini & Scott A. Vanstone, 1996. "Codes Based on Complete Graphs," Springer Books, in: Dieter Jungnickel (ed.), Designs and Finite Geometries, pages 159-165, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-1395-3_11
    DOI: 10.1007/978-1-4613-1395-3_11
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