相关论文: New construction of APN quaratic
In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.
Starting from special near-bent functions in dimension 2t-1 we construct bent functions in dimension 2t having a specific derivative. We deduce new famillies of bent functions
A strong consequence of quadratic forms becoming hyperbolic over the function field of a form is established. This result is invoked to obtain a new characterisation of hyperbolicity over function fields, and to recover a number of…
We exhibit a simplified version of the construction of a field of Morley rank p with a predicate of rank p-1, extracting the main ideas for the construction from previous papers and refining the arguments. Moreover, an explicit…
New expansionary and rotational quadratic forms are constructed for $E^n$-endomorphisms. Relations amongst the various eigenvalues, eigendirections and matrix invariants are established, including propositions on complexity and geometric…
In this paper disprove a conjecture by Pal and Budaghyan (DCC, 2024) on the existence of a family of APN permutations, but showing that if the field's cardinality $q$ is larger than~$9587$, then those functions will never be APN. Moreover,…
The single trivariate representation proposed in [C. Beierle, C. Carlet, G. Leander, L. Perrin, A Further Study of Quadratic APN Permutations in Dimension Nine, arXiv:2104.08008] of the two sporadic quadratic APN permutations in dimension 9…
We survey current term-wise techniques for quadratizing high-degree pseudo-Boolean functions and introduce a new one, which allows multiple splits of terms. We also introduce the first aggregative approach, which splits a collection of…
The {\em abeliant} is a polynomial rule for producing an $n$ by $n$ matrix with entries in a given ring from an $n$ by $n$ by $n+2$ array of elements of that ring. The theory of abeliants, first introduced in an earlier paper of the author,…
Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.
We provide some applications of a polynomial criterion for difference sets. These include counting the difference sets with specified parameters in terms of Hilbert functions, in particular a count of bent functions. We also consider the…
A new unifying theory was recently proposed by the author in the publication "Arrangement field theory - beyond strings and loop gravity -". Such theory describes all fields (gravitational, gauge and matter fields) as entries in a matricial…
The aim of this note is to give a proof of Theorem A from our work on the geometric Northcott property in the simpler case of the quadratic family; being in dimension $1$ in both the dynamical space and the parameter space, and having a…
In 2018, Pott, at al. have studied in [IEEE Transactions on Information Theory. Volume: 64, Issue: 1, 2018] the maximum number of bent components of vectorial function. They have presented serval nice results and suggested several open…
In this paper, we establish a lower bound on the total number of inequivalent APN functions on the finite field with $2^{2m}$ elements, where $m$ is even. We obtain this result by proving that the APN functions introduced by Pott and the…
In the first part of this paper [16], some results on how to compute the flat spectra of Boolean constructions w.r.t. the transforms {I,H}^n, {H,N}^n and {I,H,N}^n were presented, and the relevance of Local Complementation to the quadratic…
The number of $n$-ary bent functions is less than $2^{3\cdot2^{n-3}(1+o(1))}$ as $n$ is even and $n\rightarrow\infty$. Keywords: Boolean function, bent function, upper bound
Dobbertin, Mills, M\"uller, Pott and Willems conjecture that two families of power mapping are families of APN functions. Here we prove those two conjectures.
In this paper we find the genus field of finite abelian extensions of the global rational function field. We introduce the term conductor of constants for these extensions and determine it in terms of other invariants. We study the…
In the present work we explore relationships between multiplicative functions defined in \cite{Garonzi_2018}, \cite{Lazorec}. To do so, we use other important quotients defined and studied in \cite{ndeg}, \cite{Marius}, thus establishing…