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The relation between the Walsh-Hadamard transform and the autocorrelation function of Boolean functions is used to study propagation characteristics of these functions. The Strict Avalanche Criterion and the Perfect Nonlinearity Criterion are generalized in a Propagation Criterion of degree k. New properties and constructions for Boolean bent functions are given and also the extension of the definition to odd values of n is discussed. New properties of functions satisfying higher order SAC are derived. Finally a general framework is established to classify functions according to their propagation characteristics if a number of bits is kept constant.