Amela Muratović-Ribić

Vectorial Bent Functions From Multiple Terms Trace Functions

In this paper, we provide necessary and sufficient conditions for a function of the form F(x)=Trk^2k(Σi=1^taix^ri(2k-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 bentness and the evaluation of F on the cyclic group of the (2^k+1)th primitive roots of unity in GF(2^2k). More precisely, for this group of cardinality 2^k+1 given by U={u ∈ GF(2^2k):u^2k+1=1}, it is shown that the property of being vectorial bent implies that Im(F)=GF(2^k)∪{0}, if F is evaluated on U, that is, F(u) takes all possible values of GF(2^k)* exactly once and the zero value is taken twice when u ranges over U. This condition is then reformulated in terms of the evaluation of certain elementary symmetric polynomials related to F, which in turn gives some necessary conditions on the coefficients ai (for binomial trace functions) that can be stated explicitly. Finally, we show that a bent trace monomial of Dillons type Trk^2k(λx^r(2k-1)) is never a vectorial bent function.

A note on the coefficients of inverse polynomials

We describe some relations on the coefficients of a polynomial in terms of the map that induces and use them to characterize the coefficients of the inverse polynomials of some special classes of permutation polynomials.

Vectorial Hyperbent Trace Functions From the \(\mathcal {PS}_{\rm ap}\) Class—Their Exact Number and Specification

To identify and specify trace bent functions of the form Tr(P(x)), where P(x) ∈ F(2ⁿ)[x], has been an important research topic lately. We characterize a class of vectorial (hyper)bent functions of the form F(x) = Tr_kⁿ (Σ_i=0(2^k) a_ixⁱ⁽(2^k)^-1)), where n = 2k, in terms of finding an explicit expression for the coefficients a_i so that F is vectorial hyperbent. These coefficients only depend on the choice of the interpolating polynomial used in the Lagrange interpolation of the elements of U and some prespecified outputs, where U is the cyclic group of (2^n/2 + 1)th roots of unity in F(2ⁿ). We show that these interpolation polynomials can be chosen in exactly (2^k + 1)!2^k-1 ways and this is the exact number of vectorial hyperbent functions of the form Tr_kⁿ (Σ_i=0^2k a_ixⁱ⁽(2^k)^-1)). Furthermore, a simple optimization method is proposed for selecting the interpolation polynomials that give rise to trace polynomials with a few nonzero coefficients.

On a conjecture of polynomials with prescribed range

We show that, for any integer

Modelling constraints in school timetabling using integer linear programming

\ell

On coefficients of polynomials over finite fields

with

On derivatives of polynomials over finite fields through integration

q-\sqrt{p} -1 \leq \ell 9

On derivatives of planar mappings and their connections to complete mappings

, there exists a multiset

REDOSPLAT: A readable domain-specific language for timetabling requirements definition

M

The multisubset sum problem for finite abelian groups

satisfying that