Resilient function is a natural generalization of correlation immunity Boolean function.This paper discusses balanced resilient functions

with following results:a kind of structure of balanced resilient functions is presented

and therefore a method is given which constructs balanced (

n+1

m

2t+1

) resilient functions from balanced (

n

m

2t

) resilient functions;a proposition is given and proved that the resilient order of the balanced linear function equals the mini-weight of corresponding block code minus one

and the supremum of this order can often be reached by non-linear functions.