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pro vyhledávání: '"Topuzoglu A"'
We introduce a new concept, the APN-defect, which can be thought of as measuring the distance of a given function $G:\mathbb{F}_{2^n} \rightarrow \mathbb{F}_{2^n}$ to the set of almost perfect nonlinear (APN) functions. This concept is motivated by t
Externí odkaz:
http://arxiv.org/abs/2406.07468
Autor:
Anbar, Nurdagül, Oduzak, Almasa, Patel, Vandita, Quoos, Luciane, Somoza, Anna, Topuzoğlu, Alev
The well-known Chowla and Zassenhaus conjecture, proven by Cohen in 1990, states that if $p>(d^2-3d+4)^2$, then there is no complete mapping polynomial $f$ in $\Fp[x]$ of degree $d\ge 2$. For arbitrary finite fields $\Fq$, a similar non-existence res
Externí odkaz:
http://arxiv.org/abs/1703.08086
Autor:
Işık, Leyla, Topuzoğlu, Alev
Most results on the value sets $V_f$ of polynomials $f \in \mathbb{F}_q[x]$ relate the cardinality $|V_f|$ to the degree of $f$. In particular, the structure of the spectrum of the class of polynomials of a fixed degree $d$ is rather well known. We c
Externí odkaz:
http://arxiv.org/abs/1701.06158
The well-known Chowla and Zassenhaus conjecture, proven by Cohen in 1990, states that for any $d\ge 2$ and any prime $p>(d^2-3d+4)^2$ there is no complete mapping polynomial in $\mathbb{F}_{p}[x]$ of degree $d$. For arbitrary finite fields $\mathbb{F
Externí odkaz:
http://arxiv.org/abs/1604.07710
The Walsh transform $\widehat{Q}$ of a quadratic function $Q:F_{p^n}\rightarrow F_p$ satisfies $|\widehat{Q}(b)| \in \{0,p^{\frac{n+s}{2}}\}$ for all $b\in F_{p^n}$, where $0\le s\le n-1$ is an integer depending on $Q$. In this article, we study the
Externí odkaz:
http://arxiv.org/abs/1603.04685
Publikováno v:
In Finite Fields and Their Applications March 2020 63
Publikováno v:
In Finite Fields and Their Applications July 2019 58:124-132
Akademický článek
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Autor:
Anbar, Nurdagül, Odz̆ak, Almasa, Patel, Vandita, Quoos, Luciane, Somoza, Anna, Topuzoğlu, Alev
Publikováno v:
In Finite Fields and Their Applications January 2018 49:132-142