We give new proofs of asymptotic upper bounds of coding theory obtained
within the frame of Delsarte's linear programming method. The proofs rely on
the analysis of eigenvectors of some finite-dimensional operators related to
orthogonal polynomials. The examples of the method considered in the paper
include binary codes, binary constant-weight codes, spherical codes, and codes
in the projective spaces.Comment: 11 pages, submitte