Highly nonlinear balanced Boolean functions with good local and global avalanche characteristics

Here we deal with an interesting subset of n-variable balanced Boolean functions which satisfy strict avalanche criteria. These functions achieve the sum-of-square indicator value (a measure for global avalanche criteria) strictly less than 2²ⁿ⁺¹ and nonlinearity strictly greater than 2ⁿ⁻¹−2^⌊n/2⌋. These parameters are currently best known. Moreover, these functions do not possess any nonzero linear structure. The technique involves a well-known simple construction coupled with very good initial functions obtained by computer search, which were not known earlier.