Krawtchouk polynomials

Summary

The Krawtchouk (or Kravchuk) polynomials $K_n(x; p, N)$ are the orthogonal polynomials of the binomial distribution on $\set{0, 1, \dots, N}$. They are a finite family: there is one polynomial for each degree $n = 0, \dots, N$. In coding theory they describe the Hamming scheme, and they enter the MacWilliams identities and Delsarte's linear programming bound.