A system of polynomials for the complex hamming spaces

It is known that polynomials f(t), such that the matrix f(rho(x,y)) with the Hamming distance rho(x,y) between vectors x=(x
₁
,...,x
_n
) and y=(y
₁
,...,y
_n
) is nonnegative definite, are described with the help of the system of Krawtchouk polynomials. In the paper the question on the existence of a similar system of polynomials is considered when the function rho(x,y) is not the Hamming distance