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Probl. Peredachi Inf., 2015, Volume 51, Issue 3, Pages 31–40 (Mi ppi2178)  

Coding Theory

Reconstruction of eigenfunctions of a $q$-ary $n$-dimensional hypercube

A. Yu. Vasil'eva

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: We prove that values of an arbitrary eigenfunction of a $q$-ary $n$-dimensional hypercube can be uniquely reconstructed at all vertices inside a ball if its values on the corresponding sphere are known; we give sufficient conditions for such reconstruction in terms of the eigenvalue and the ball radius. We show that in the case where values of an eigenfunction are given on a sphere of radius equal to the corresponding eigenvalue, all values of the eigenfunction can be reconstructed; similarly to the previous case, sufficient numerical conditions are presented.

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English version:
Problems of Information Transmission, 2015, 51:3, 231–239

Bibliographic databases:

UDC: 621.391.1+519.1
Received: 16.12.2014
Revised: 30.04.2015

Citation: A. Yu. Vasil'eva, “Reconstruction of eigenfunctions of a $q$-ary $n$-dimensional hypercube”, Probl. Peredachi Inf., 51:3 (2015), 31–40; Problems Inform. Transmission, 51:3 (2015), 231–239

Citation in format AMSBIB
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\by A.~Yu.~Vasil'eva
\paper Reconstruction of eigenfunctions of a~$q$-ary $n$-dimensional hypercube
\jour Probl. Peredachi Inf.
\yr 2015
\vol 51
\issue 3
\pages 31--40
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\transl
\jour Problems Inform. Transmission
\yr 2015
\vol 51
\issue 3
\pages 231--239
\crossref{https://doi.org/10.1134/S0032946015030035}
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  • Проблемы передачи информации Problems of Information Transmission
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