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Nonbinary Error-Correcting Codes with One-Time Error-Free Feedback

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Abstract

We show that, using one-time error-free feedback, it is possible to attain the asymptotic Hamming bound if the number of errors is fixed.

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REFERENCES

  1. Yekhanin, S. and Dumer, I., Long Nonbinary Codes Exceeding the Gilbert-Varshamov Bound for any Fixed Distance, IEEE Trans. Inform. Theory, 2004, vol. 50, no.10, pp. 2357–2362.

    Google Scholar 

  2. Kabatyanskii, G.A. and Panchenko, V.I., Unit Sphere Packings and Coverings of the Hamming Space, Probl. Peredachi Inf., 1988, vol. 24, no.4, pp. 3–16 [Probl. Inf. Trans. (Engl. Transl.), 1988, vol. 24, no. 4, pp. 261–272].

    Google Scholar 

  3. Berlekamp, E.R., Block Coding with Noiseless Feedback, PhD Thesis, MIT, Cambridge, 1964 (see also Berlekamp, E.R., Block Coding for the Binary Symmetric Channel with Noiseless, Delayless Feedback, Error-Correcting Codes, Mann, H.B., Ed., New York: Wiley, 1969, pp. 61–85 [Russian Transl. in Kibern. Sb. Nov. Ser., vol. 9, Moscow: Mir, 1972, pp. 5–29]).

    Google Scholar 

  4. Zingangirov, K.Sh., On the Number of Correctable Errors for Transmission over a Binary Symmetrical Channel with Feedback, Probl. Peredachi Inf., 1976, vol. 12, no.2, pp. 3–19 [Probl. Inf. Trans. (Engl. Transl.), 1976, vol. 12, no. 2, pp. 85–97].

    Google Scholar 

  5. Zinoviev, V.A. and Katsman, G.L., Universal Code Families, Probl. Peredachi Inf., 1993, vol. 29, no.2, pp. 3–8 [Probl. Inf. Trans. (Engl. Transl.), 1993, vol. 29, no. 2, pp. 95–100].

    Google Scholar 

  6. Cicalese, F., Mundici, D., and Vaccaro, U., Least Adaptive Optimal Search with Unreliable Tests, Theor. Comp. Sci., 2004, vol. 270, no.1–2, pp. 877–893.

    Google Scholar 

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Translated from Problemy Peredachi Informatsii, No. 2, 2005, pp. 63–67.

Original Russian Text Copyright © 2005 by Bassalygo.

Supported in part by the Russian Foundation for Basic Research, project no. 03-01-00098.

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Bassalygo, L.A. Nonbinary Error-Correcting Codes with One-Time Error-Free Feedback. Probl Inf Transm 41, 125–129 (2005). https://doi.org/10.1007/s11122-005-0017-3

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  • DOI: https://doi.org/10.1007/s11122-005-0017-3

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