Journée-séminaire de combinatoire

(équipe CALIN du LIPN, université Paris-Nord, Villetaneuse)

Le 12 avril 2016 à 14h00 en B107, Valentin Suder nous parlera de : Antiderivative functions over F_2^n

Résumé : We use a linear algebra point of view to describe the derivatives and higher order derivatives over F_2^n. On one hand, this new approach ennobles us to prove several properties of these functions, as well as the functions that have these derivatives. On the other hand, we provide a method to construct all of the higher order derivatives in given directions. We also demonstrate some properties of the higher order derivatives and their decomposition as a sum of functions with 0-linear structure. Moreover, we introduce a criterion and an algorithm to realize discrete antidifferentiation of vectorial Boolean functions. This leads us to define a new equivalence of functions, that we call differential equivalence, which links functions that share the same derivatives in directions given by some subspace.


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