Lower bound for the complexity of five-valued polarized polynomials

The paper is devoted to the complexity of representation of $q$-valued functions by polarized polynomials and by matrix Kronecker forms of certain type. The complexity of a function is the minimal possible number of nonzero coefficients of a polynomial or a Kronecker form representing the function. It is known that for polynomial representation and representation by Kronecker forms of a certain type the maximal values of complexity in the class of all $q$-valued $n$-ary functions coincide. We establish the lower bound of these maximal values for five-valued functions.