Improved estimates for the number of (n, m, k)-resilient and correlation-immune boolean mappings
Improved lower and upper bounds for |K (n, m, k)| (the number of correlation-immune of order k binary mappings) and |R (m,n, k)| (the number of (n, m, k)-resilient binary map-kn pings) are obtained. By M (n, k) we denote , and by T (n, m, k) - the expres- s=0 уs / sion (2m - 1) П - k + M (n, k) log2 . If m > 5 and k (5 + 2log2n) + 6m 0 such that, for any e1 ,e2 and n > n0, m2 - m - 12 2 +17 M (n, k) - £1 2 |R (n, m, k)| - m2n + T (n, m, k) m 4 - m + 3) M (n, k) + e2. If m > 5 and k (5 + 2log2n) + 6m 0 such that, for any e1,e2 and n > n0, m2 - m - 12 2 +17 M (n, k) - £1 2 |K (n, m, k) | - m2n + m2m 1 + T (n, m, k) - n + 1 + log2 n 2 (2m - 1) m-4 - m + 3) M (n, k) + £2.