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Multiplied Complete Fix-Free Codes and Shiftings Regarding the 3/4-Conjecture

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Information Theory, Combinatorics, and Search Theory

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7777))

Abstract

Given a nonnegative sequence α of integers with Kraftsum at most 3/4, Ahlswede, Balkenhol and Khachatrian proposed the existence of a fix-free code with exactly α n words for any length n. In this article complete thin fix-free codes are constructed and both so-called n-closed systems and multiplication are used to enlarge this class. In addition, a sufficient criterion is given in terms of elementary sequence-shifting preserving the fix-freedom of the associated code.

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References

  1. Ahlswede, R., Balkenhol, B., Khachatrian, L.: Some properties of fix-free codes. In: Proc. Int. Seminar Coding Theory and Combinator, Thahkadzor, Armenia, pp. 20–33 (1996)

    Google Scholar 

  2. Berstel, J., Perrin, D.: Theory of Codes. Academic Press, Orlando (1985)

    MATH  Google Scholar 

  3. Deppe, C., Schnettler, H.: On q-ary fix-free codes and directed deBruijn graphs. In: Proc. Int. Symp. Inf. Theory, Seattle, WA, pp. 1482–1485 (2006)

    Google Scholar 

  4. Harada, K., Kobayashi, K.: A note on the fix-free code property. IEICE Trans. Fundamentals E82-A(10), 2121–2128 (1999)

    Google Scholar 

  5. Khosravifard, M., Halabian, H., Gulliver, T.A.: A Kraft-type sufficient condition for the existence of D-ary fix-free codes. IEEE Trans. Inf. Theory 56(6), 2920–2927 (2010)

    Article  MathSciNet  Google Scholar 

  6. Kukorelly, Z., Zeger, K.: Sufficient conditions for existence of binary fix-free codes. IEEE Trans. Inf. Theory 51(10), 3433–3444 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Schnettler, H.: On the \(\frac{3}{4}\)-conjecture for fix-free codes: a survey. arXiv:0709.2598v1 [cs.IT]

    Google Scholar 

  8. Ye, C., Yeung, R.W.: Some basic properties of fix-free codes. IEEE Trans. Inf. Theory 47(1), 72–87 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Yekhanin, S.: Sufficient conditions of existence of fix-free codes. In: Proc. Int. Symp. Inf. Theory, Washington D.C, p. 284 (2001)

    Google Scholar 

  10. Yekhanin, S.: Improved upper bound for the redundancy of fix-free codes. IEEE Trans. Inf. Theory 50(11), 2815–2818 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Rheinisch-Westfälische Technische Hochschule Aachen, Templergraben 55, 52062, Aachen, Germany

    Michael Bodewig

Authors
  1. Michael Bodewig
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bielefeld, Universitätsstr. 25, 33615, Bielefeld, Germany

    Harout Aydinian  & Christian Deppe  & 

  2. Department of Computer Science, University of Salerno, via Ponte don Melillo, 84084, Fisciano, Italy

    Ferdinando Cicalese

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Bodewig, M. (2013). Multiplied Complete Fix-Free Codes and Shiftings Regarding the 3/4-Conjecture. In: Aydinian, H., Cicalese, F., Deppe, C. (eds) Information Theory, Combinatorics, and Search Theory. Lecture Notes in Computer Science, vol 7777. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36899-8_35

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  • DOI: https://doi.org/10.1007/978-3-642-36899-8_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36898-1

  • Online ISBN: 978-3-642-36899-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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