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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>(Σi=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 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)

In this paper we find an exact formula for the number of partitions of an element z into m parts over a finite field, i.e. we find the number of nonzero solutions of the equation x 1 + x 2 + · · · + x m = z over a finite field when the order of terms does not matter. This is equivalent to counting the number of m-multi-subsets whose sum is z. When the order… (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)

Integer linear programming is a popular method of generating school timetables. Although computationally simpler, school timetabling is less developed area than university timetabling, because the models which resolve timetabling problems proposed thus far have been adjusted to individual cases differing from country to country. A proposed model meets most… (More)

For any given polynomial f over the finite field Fq with degree at most q − 1, we associate it with a q × q matrix A(f) = (a ik) consisting of coefficients of its powers (f (x)) k = q−1 i=0 a ik x i modulo x q −x for k = 0, 1,. .. , q −1. This matrix has some interesting properties such as A(g • f) = A(f)A(g) where (g • f)(x) = g(f (x)) is the composition… (More)

To identify and specify trace bent functions of the form Tr(P(x)), where P(x) ∈ 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> (Σ<sub>i=0(</sub>2<sup>k</sup>) a<sub>i</sub>x<sup>i(</sup>(2<sup>k</sup>)<sup>-1)</sup>),… (More)