3 research outputs found
The Divisibility Modulo 4 of Kloosterman Sums over Finite Fields of Characteristic 3
Recently Garashuk and Lisonek evaluated Kloosterman sums
K (a) modulo 4 over a finite field F3m in the case of even K (a). They posed it as an open
problem to characterize elements a in F3m for which K (a) ≡ 1 (mod4) and K (a) ≡ 3 (mod4). In
this paper, we will give an answer to this problem. The result allows us to count the number of
elements a in F3m belonging to each of these two classes
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