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Reconstruction theorems for centered functions and perfect codes

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Abstract

The article addresses the centered functions and perfect codes in the space of all binary n-tuples. We prove that all values of a centered function in a ball of radius k ≤ (n + 1)/2 are uniquely defined from its radial sums with respect to the vertices of the corresponding sphere. We present some theorems of full and partial reconstruction of a centered function from part of its values and derive a new property of the symmetry groups of centered functions.

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References

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

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

Authors
  1. S. V. Avgustinovich
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  2. A. Yu. Vasil’eva
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Corresponding author

Correspondence to S. V. Avgustinovich.

Additional information

Original Russian Text Copyright © 2008 Avgustinovich S. V. and Vasil’eva A. Yu.

The authors were partially supported by the Russian Foundation for Basic Research (Grant 07-01-00248-a) and Novosibirsk State University.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 3, pp. 483–489, May–June, 2008.

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Avgustinovich, S.V., Vasil’eva, A.Y. Reconstruction theorems for centered functions and perfect codes. Sib Math J 49, 383–388 (2008). https://doi.org/10.1007/s11202-008-0037-5

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  • DOI: https://doi.org/10.1007/s11202-008-0037-5

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