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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.

##### MSC:
 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
##### Keywords:
covering codes; epsilon entropy; ellipsoids; Hamming space
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