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Non-Boolean almost perfect nonlinear functions on non-Abelian groups
The purpose of this paper is to present the extended definitions and
characterizations of the classical notions of APN and maximum nonlinear Boolean
functions to deal with the case of mappings from a finite group K to another
one N with the possibility that one or both groups are non-Abelian.Comment: 17 page
On the dual of (non)-weakly regular bent functions and self-dual bent functions
For weakly regular bent functions in odd characteristic the dual
function is also bent. We analyse a recently introduced construction of nonweakly
regular bent functions and show conditions under which their dual is
bent as well. This leads to the denition of the class of dual-bent functions
containing the class of weakly regular bent functions as a proper subclass. We
analyse self-duality for bent functions in odd characteristic, and characterize
quadratic self-dual bent functions. We construct non-weakly regular bent functions
with and without a bent dual, and bent functions with a dual bent function
of a dierent algebraic degree
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