Abstract: In this paper, a new generalized construction method for correlation immune Boolean function satisfying PC(l) of order k is provided. The construction is based on the use of linear error-correcting codes together with bijective functions. Furthermore, some new construction methods for (n , m , t) resilient functions satisfying PC(l) of order k is also discussed. In addition, the authors also show that these functions have many other good cryptographic properties such as high nonlinearity, good algebraic degree and so on .