The present work uses estimates and inequalities with sums of binomial coefficients to solve some problems in coding theory and cryptography. We consider the existence problem for codes uniformly distributed in balls with degree l, and the problem of existence for l-packings of big radius. We also solve the existence problem for a class of special type matrices introduced by Yu.V.Tarannikov, which are used for constructing stable functions with cryptographically optimal parameters.

coding theory, cryptography, binomial coefficient sums, small size codes, l-packings of big radius

Mathematical problems and theory of numerical methods