A Boolean function is said to be correlation immune if its output leaks no information about its input values.Such functions have extensive applications in computer security practices.This paper studies the construction and enumeration problem for

m

th-order correlation immune functions and presents two new construction methods.Furthermore

we compare new methods with Seigenthaler

Yang

Camion

Seberry

Wen et al’s and show that new methods actually generalize relational conclusions in these references.Using new methods not only can construct directly

m

th-order correlation-immune functions

but also can construct new correlation immune functions on the basis of known correlation immune functions.In addition

based on new construction methods

the enumeration lower bound of balanced

m

th-order correlation im

mune functions is improved.