  Krawtchouk polynomials appear in a variety of contexts, most notably as
orthogonal polynomials and in coding theory via the Krawtchouk transform. We
present an operator calculus formulation of the Krawtchouk transform that is
suitable for computer implementation. A positivity result for the Krawtchouk
transform is shown. Then our approach is compared with the use of the
Krawtchouk transform in coding theory where it appears in MacWilliams' and
Delsarte's theorems on weight enumerators. We conclude with a construction of
Krawtchouk polynomials in an arbitrary finite number of variables, orthogonal
with respect to the multinomial distribution.
