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Frames as Continuous Redundant Codes

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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.

Funding

The work is supported by the grant of the Russian Government, agreement no. 14.W03.31.0031.

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Correspondence to Al. R. Valiullin, Ar. R. Valiullin or V. V. Galatenko.

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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

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