Boolean Functions Satisfying Higher Order Propagation Criteria
Boolean functions that satisfy higher order propagation criteria are studied. A complete characterization is given of the autocorrelation function and Walsh spectrum of second order functions. The number of second order functions satisfying PC(k) is related to a problem in coding theory and can be computed explicitly for k = 1, n − 1 and n. A new interpretation of the number of balanced second order functions is given and a class of functions showing interesting properties is discussed.
KeywordsAutocorrelation Function Boolean Function Order Function Bend Function Balance Function
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