On cryptographic propagation criteria for Boolean functions

We characterize those functions on GF(2)/sup n/ which satisfy the propagation criterion of degree n-2. We give a general construction of nonquadratic functions satisfying the extended propagation criterion of degree l and order k, which uses the existence of nonlinear, systematic codes with good minimum distances and dual distances. We apply it to Kerdock codes and Preparata codes. We also study the other cryptographic properties of the functions obtained this way.