Abstract
The asymptotic behavior of the ε-entropy of ellipsoids in an n-dimensional Hamming space whose coefficients take only two different values is investigated as n → ∞. Explicit expressions for the main terms of the asymptotic expansion of ε-entropy of such ellipsoids are obtained under various relations between ε and parameters that define these ellipsoids.
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REFERENCES
1. Pinsker, M.S., Entropy of an Ellipsoid in a Hamming Space, Probl. Peredachi Inf., 2000, vol. 36, no. 4, pp. 47–52 [Probl. Inf. Trans. (Engl. Transl.), 2000, vol. 36, no. 4, pp. 325-330].
Dumer, I.I., Pinsker, M.S., and Prelov, V.V., Epsilon-entropy of an Ellipsoid in a Hamming Space, Probl. Peredachi Inf., 2002, vol. 38, no. 1, pp. 3–18 [Probl. Inf. Trans. (Engl. Transl.), 2002, vol. 38, no. 1, pp. 1-15].
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Prelov, V.V., van der Meulen, E.C. On the Epsilon-entropy of One Class of Ellipsoids in a Hamming Space. Problems of Information Transmission 38, 113–125 (2002). https://doi.org/10.1023/A:1020006609599
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DOI: https://doi.org/10.1023/A:1020006609599