The class of \(n\)-valued functions having subfunctions of special form (Q1878551)

The paper deals with \(n\)-valued functions of \(k\) variables which are correlation immune of order \(k-1\) and do not have subfunctions of two variables reducible to the symmetric permutations of the values of each of the variables. It is shown that such functions exist for \(n\geq 5\) for all \(k\geq 2\) and do not exist for \(n<5\).