  Polynomial, or Delsarte's, method in coding theory accounts for a variety of
structural results on, and bounds on the size of, extremal configurations
(codes and designs) in various metric spaces. In recent works of the authors
the applicability of the method was extended to cover a wider range of problems
in coding and information theory. In this paper we present a general framework
for the method which includes previous results as particular cases. We explain
how this generalization leads to new asymptotic bounds on the performance of
codes in binary-input memoryless channels and the Gaussian channel, which
improve the results of Shannon et al. of 1959-67, and to a number of other
results in combinatorial coding theory.
