对线性等价意义下2个布尔函数的密码学性质的异同做了进一步的分析，得到了一个布尔函数线性等价于某个具有m阶相关免疫性的布尔函数的充分必要条件和线性等价于某个满足k次扩散准则的布尔函数的充分必要条件，在线性等价意义上，给出了由不具有相关免疫性且不满足扩散准则的布尔函数，构造既具有相关免疫性、也满足扩散准则的布尔函数的实例。

The paper made an analysis of the similarities and differences about the cryptographic properties of two Boolean functions in the sense of linearly equivalence, and obtained a sufficient and necessary condition about a Boolean function linearly equivalent to some m order correlation-immune Boolean function. It also obtained a sufficient and necessary condition about a Boolean function linearly equivalent to some Boolean function satisfying the k order propagation criterion. Moreover, it showed an example,in which a given Boolean function, that is not correlation-immuned and does not satisfy the propagation criterion can be constructed into a correlation-immuned Boolean function that can satisfy the propagation criterion and is linearly equivalent to the former one.