This article is cited in 6 papers

Theoretical Foundations of Applied Discrete Mathematics

On the coincidence of the class of bent-functions with the class of functions which are minimally close to linear functions

V. I. Solodovnikov

Academy of Criptography of Russia, Moscow, Russia

Abstract: For functions from $(\mathbb Z/(p))^n$ to $(\mathbb Z/(p))^m$ where $p$ is a prime, the property of closeness to linear functions is investigated. It is proved that, for any function, this property is inherited by its homomorphic images. As a generalization of an analogous statement for Boolean functions it is shown that if $p=2$ or $3$ then the class of functions which are absolutely minimally close to linear ones coincides with the class of bent-functions.

Keywords: functions closeness, absolutely non-homomorphic functions, minimal functions, bent-functions.

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