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Testing Sets for 1-Perfect Code

  • S. V. Avgustinovich
  • A. Yu. Vasil’eva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4123)

Abstract

This paper continues the research of [1,2]. In [1] it was shown that a 1-perfect code is uniquely determined by its vertices at the middle levels of hypercube and in [2] the concerned formula was obtained. Now we prove that the vertices at the r-th level, r≤(n–1)/2, of such a code of length n uniquely determine all code vertices at the lower levels.

Keywords

Operation Research Block Code Middle Level Induction Supposition Common Vertex 
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References

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    Avgustinovich, S.V.: On a property of perfect binary codes. Discrete Analysis and Operation Research (in Russian) 2(1), 4–6 (1995)MathSciNetGoogle Scholar
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    Avgustinovich, S.V., Vasil’eva, A.Y.: Reconstruction of centered functions by its values on two middle levels of hypercube. Discrete Analysis and Operation Research (in Russian) 10(2), 3–16 (2003)MATHMathSciNetGoogle Scholar
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    Lloyd, S.P.: Binary block coding. Bell Syst. Techn. J. 36(2), 517–535 (1957)MathSciNetGoogle Scholar
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    Vasil’eva, A.Y.: Local spectra of perfect binary codes. Discrete Analysis and Operation Research (in Russian) 6(1), 16–25 (1999)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • S. V. Avgustinovich
  • A. Yu. Vasil’eva

There are no affiliations available

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