Abstract: In this paper, the vectors set called complete set is presented. A class of second order ergodic matrix is constructed by using the complete set, and a class of third order ergodic matrix is also constructed by using the partial set of complete set. On the basis mentioned above, the corresponding Boolean functions with second order and with third order correlation immunities are given. The paper also proves that the additional column vector is not allowed for both second order and third order ergodic matrices so constructed.