Reconstruction theorems for centered functions and perfect codes |
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Authors: | S V Avgustinovich A Yu Vasil’eva |
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Institution: | (1) Sobolev Institute of Mathematics, Novosibirsk, Russia |
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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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Keywords: | centered function perfect code discrete Fourier transform |
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