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Bent functions from a finite abelian group into a finite abelian group

V. I. Solodovnikov


Abstract: 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, a function is uniquely determined by the distances to homomorphisms with shifts, and that in the primary case the bent functions are absolutely minimal.

UDC: 519.7

Received: 18.02.2000
Revised: 13.02.2001

DOI: 10.4213/dm234

 English version: Discrete Mathematics and Applications, 2002, 12:2, 111–126

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