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Kravchuk
Kravchuk is a surname that derived from the occupation of tailor with addition of a common Ukrainian suffix -chuk.
Kravchuk polynomials
Kravchuk polynomials or Krawtchouk polynomials are discrete orthogonal polynomials associated with the binomial distribution, introduced by Mikhail Kravchuk (1929). The first few polynomials are (for q=2): K 0 ( x ; n ) = 1 {\displaystyle {\mathcal {K}}_{0}(x;n)=1} K 1 ( x ; n ) = − 2 x + n {\displaystyle {\mathcal {K}}_{1}(x;n)=-2x+n} K 2 ( x ; n ) = 2 x 2 − 2 n x + ( n 2 ) {\displaystyle {\mathcal {K}}_{2}(x;n)=2x^{2}-2nx+{n \choose 2}} K 3 ( x ; n ) = − 4 3 x 3 + 2 n x 2 − ( n 2 − n + 2 3 ) x + ( n 3 ) .
Krawtchouk matrices
In mathematics, Krawtchouk matrices are matrices whose entries are values of Krawtchouk polynomials at nonnegative integer points. The Krawtchouk matrix K is an (N+1)×(N+1) matrix.