Asymptotics of the ϵ-entropy for a certain class of ellipsoids in a Hamming space

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 representation for the ε-entropy of such ellipsoids are obtained under different relations between ε and parameters defining these ellipsoids.