An Optimization Problem Related to the Computation of the Epsilon-entropy of an Ellipsoid in a Hamming Space

The problem of optimizing (finding the maximin of) the difference between the entropy functions of two $n$-dimensional vectors under special restrictions on their components is solved. This optimum gives the main term of the asymptotics for the $\varepsilon$-entropy of an ellipsoid in a Hamming space as the dimension of the space grows.