Nonlinearity, Local and Global Avalanche Characteristics of Balanced   Boolean Functions
  First, we construct a class of functions with good local avalanche characteristics, but bad global avalanche characteristics. We also derive some bounds for the nonlinearity of such functions. It improves upon the results of Son et al., and Sung et al. In our second result we construct a class of highly nonlinear balanced functions with good local and global avalanche characteristics. 
Pantelimon Stanica