A new upper bound for the length of snakes


Ad-dimensional circuit code of spreads is a simple circuitC in the graph of thed-dimen sional unit cube with the property that for any verticesx andy ofC which differ in exactlyr co-ordinates,r<s, there exists a path fromx toy consisting ofr edges ofC. This property is useful for detecting and limiting errors. In this paper we give a new upper bound for the maximum length of ad-dimensional circuit code of spread 2.

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  1. [1]

    H. L. Abbott, A Note on the Snake-in-the-Box Problem, unpublished manuscript.Some Problems in Combinatorial Analysis, Ph. D. thesis, University of Alberta, Edmonton, Canada, 1965.

    Google Scholar 

  2. [2]

    L. Danzer andV. Klee, Length of Snakes in Boxes,J. Combinatorial Theory 2 (1967), 258–265.

    MATH  MathSciNet  Google Scholar 

  3. [3]

    R. J. Douglas, Upper Bounds on the Length of Circuits of Even Spread in thed-Cube,J. Combinatorial Theory 7 (1969), 206–214.

    MATH  MathSciNet  Google Scholar 

  4. [4]

    V. V. Glagolev, An Upper Estimate of the Length of a Cycle in then-Dimensional Unit Cube (Russian),Diskretnyi Analiz 6 (1966), 3–7.

    MATH  MathSciNet  Google Scholar 

  5. [5]

    W. H. Kautz, Unit-Distance Error-Checking Codes,IRE Trans. Electronic Computers 3 (1958), 179–180.

    Article  Google Scholar 

  6. [6]

    V. Klee, The Use of Circuit Codes in Analog-to-Digital Conversion,Graph Theory and its Applications (ed. B. Harris), Academic Press, New York, 1970, 121–132.

    Google Scholar 

  7. [7]

    D. G. Larman,Circuit Codes, unpublished, quoted from Douglas [3].

  8. [8]

    R. C. Singleton, Generalized Snake-in-the-Box Codes,IEEE Trans. Electronic Computers EC-15 (1966), 596–602.

    Article  Google Scholar 

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Deimer, K. A new upper bound for the length of snakes. Combinatorica 5, 109 (1985). https://doi.org/10.1007/BF02579373

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AMS subject classification 1980

  • 05 C 35
  • 94 B 25