On the complexity of representation of $k$-valued functions by generalised polarised polynomials

We consider generalised polarised polynomials for $k$-valued functions (for prime $k$). It is proved that each $k$-valued function is represented by some unique generalised polarised polynomial for each polarisation vector. We find upper and lower bounds for the Shannon functions of degree and length of the generalised polarised polynomials of $k$-valued functions.