Bent functions from a finite abelian group into a finite abelian group. (English. Russian original) Zbl 1047.94011

Solodovnikov, V. I.

Discrete Math. Appl. 12, No. 2, 111-126 (2002); translation from Diskretn. Mat. 14, No. 1, 99-113 (2002).

Summary: We introduce the notions of an absolutely non-homomorphic function, a minimal function (farthest from homomorphisms) and a bent function, and prove that the class of bent functions coincides with the class of absolutely non-homomorphic functions, that a function is uniquely determined by the distances to homomorphisms with shifts, and that in the primary case the bent functions are absolutely minimal.

MSC:

94A60	Cryptography
06E30	Boolean functions
20K01	Finite abelian groups