Asymptotic estimates for numbers of Boolean mappings with given cryptographic properties

For linear combinations of coordinate functions of random Boolean mapping a local limit theorem for the distribution of subsets of weights of submappings is improved. Also a local limit theorem for subsets of their spectral coefficients is proved. By means of these theorems we obtain upper and lower asymptotic estimates for numbers of correlation-immune and ($n,m,k$)-resilient Boolean mappings. Also we obtain an upper asymptotic estimate of the number of plateaued Boolean mappings.