Abstract
Expansions in a finite frame are considered as a continuous linear redundant coding. It is shown that coding of an element from an \(N\)-dimensional space with a frame consisting of \((N+M)\) elements allows detecting up to \(M\) errors and correcting up to \(\left\lfloor\dfrac{M}{2}\right\rfloor\) errors. It is also pointed out that these results are sharp. The results are direct continuous analogs of the classical statements from the discrete coding theory.
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ACKNOWLEDGMENTS
The authors thank Prof. T.P. Lukashenko and Dr. A.V. Galatenko for valuable discussions, remarks, and comments.
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The work is supported by the grant of the Russian Government, agreement no. 14.W03.31.0031.
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Translated by E. Oborin
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Valiullin, A.R., Valiullin, A.R. & Galatenko, V.V. Frames as Continuous Redundant Codes. Moscow Univ. Math. Bull. 76, 73–77 (2021). https://doi.org/10.3103/S002713222102008X
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DOI: https://doi.org/10.3103/S002713222102008X