Abstract:
This paper presents a study of perturbations of symmetric Boolean functions. In particular, it establishes a connection between exponential sums of these perturbations an...Show MoreMetadata
Abstract:
This paper presents a study of perturbations of symmetric Boolean functions. In particular, it establishes a connection between exponential sums of these perturbations and Diophantine equations of the form Σl=0n (nl)xl = 0, where xj belongs to some fixed bounded subset Γ of Z. The concepts of trivially balanced symmetric Boolean function and sporadic balanced Boolean function are extended to this type of perturbations. An observation made by Canteaut and Videau for symmetric Boolean functions of fixed degree is extended. To be specific, it is proved that, excluding the trivial cases, balanced perturbations of fixed degree do not exist when the number of variables grows. Some sporadic balanced perturbations are presented. Finally, a beautiful but unexpected identity between exponential sums for perturbations of two different symmetric Boolean functions is also included in this work.
Published in: IEEE Transactions on Information Theory ( Volume: 64, Issue: 2, February 2018)