On the Epsilon-entropy of One Class of Ellipsoids in a Hamming Space

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.