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On the epsilon-entropy of one class of ellipsoids in a Hamming space. (English. Russian original) Zbl 1027.94003
Probl. Inf. Transm. 38, No. 2, 113-125 (2002); translation from Probl. Peredachi Inf. 38, No. 2, 19-32 (2002).
Summary: The asymptotic behavior of the \(\varepsilon\)-entropy of ellipsoids in an \(n\)-dimensional Hamming space whose coefficients take only two different values is investigated as \(n\to\infty\). Explicit expressions for the main terms of the asymptotic expansion of \(\varepsilon\)-entropy of such ellipsoids are obtained under various relations between \(\varepsilon\) and parameters that define these ellipsoids. See also Zbl 1027.94002.

94A17 Measures of information, entropy
11H06 Lattices and convex bodies (number-theoretic aspects)
94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory
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