Let

V

be the space of dimension n over GF(2)

f(x)

a boolean function on

V

.In this paper

the set

U

of the vectors satisfying the propagation criteria is discussed.If deg

f(x)=n

then

U

is an empty set.For all the functions of degree 2

U

have at least half vectors of

V

.The avalanche characteristics of a class of functions is discussed.Boolean functions have no nonezero linear structure if and only if there are n linear independence vectors.Furthermore a construction of functions which satisfy propagation criteria of degree 2 is given.