Amela Muratovic-Ribic

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In this paper, we provide necessary and sufficient conditions for a function of the form F(x)=Trk<sup>2k</sup>(&#x03A3;i=1<sup>t</sup>aix<sup>ri(2k</sup>-1)) to be bent. Three equivalent statements, all of them providing both the necessary and sufficient conditions, are derived. In particular, one characterization provides an interesting link between the(More)
In this paper, we present a characterization of a semi-multiplicative analogue of planar functions over finite fields. When the field is a prime field, these functions are equivalent to a variant of a doubly-periodic Costas array and so we call these functions Costas. We prove an equivalent conjecture of Golomb and Moreno that any Costas polynomial over a(More)
In this note, using rather elementary technique and the derived formula that relates the coefficients of a polynomial over a finite field and its derivative, we deduce many interesting results related to derivatives of Boolean functions and derivatives of mappings over finite fields. For instance, we easily identify several infinite classes of polynomials(More)
We show that, for any integer m with 3 < m ≤ min{p − 1, q/2} where q = pn > 9 there exists a multiset M satisfying that 0 ∈ M has the highest multiplicity q −m and P b∈M b = 0 such that every polynomial over the finite field Fq with the prescribed range M has degree greater than q−m. This implies that Conjecture 5.1 in [6] is false over any finite field Fq(More)
To identify and specify trace bent functions of the form Tr(P(x)), where P(x) &#x2208; F(2<sup>n</sup>)[x], has been an important research topic lately. We characterize a class of vectorial (hyper)bent functions of the form F(x) = Tr<sub>k</sub><sup>n</sup> (&#x03A3;<sub>i=0(</sub>2<sup>k</sup>) a<sub>i</sub>x<sup>i(</sup>(2<sup>k</sup>)<sup>-1)</sup>),(More)