On Nonlinearity and Autocorrelation Properties of Correlation Immune Boolean Functions

+ 2 2 2 2 2 2 n n and a maximum possible algebraic degree of n − 1. Moreover, we present a detailed study on the Walsh spectra of these functions. Next we study the autocorrelation values of correlation immune and resilient Boolean functions. We provide new lower bounds and related results on the absolute indicator and sum of square indicator of autocorrelation values for low orders of correlation immunity. Recently it has been show that the nonlinearity and algebraic degree of correlation immune and resilient functions can be optimized simultaneously. Our analysis shows that under such a scenario, the sum of square indicator also attains its minimum value. We also point out the weakness of two recursive construction techniques for resilient functions in terms of autocorrelation values.