Haode Yan
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View article: A note on the differential spectrum of a class of locally APN functions
A note on the differential spectrum of a class of locally APN functions Open
Let $\gf_{p^n}$ denote the finite field containing $p^n$ elements, where $n$ is a positive integer and $p$ is a prime. The function $f_u(x)=x^{\frac{p^n+3}{2}}+ux^2$ over $\gf_{p^n}[x]$ with $u\in\gf_{p^n}\setminus\{0,\pm1\}$ was recently …
View article: A note on the differential spectrum of the Ness-Helleseth function
A note on the differential spectrum of the Ness-Helleseth function Open
Let $n\geqslant3$ be an odd integer and $u$ an element in the finite field $\gf_{3^n}$. The Ness-Helleseth function is the binomial $f_u(x)=ux^{d_1}+x^{d_2}$ over $\gf_{3^n}$, where $d_1=\frac{3^n-1}{2}-1$ and $d_2=3^n-2$. In 2007, Ness an…
View article: On correlation distribution of Niho-type decimation $d=3(p^m-1)+1$
On correlation distribution of Niho-type decimation $d=3(p^m-1)+1$ Open
The cross-correlation problem is a classic problem in sequence design. In this paper we compute the cross-correlation distribution of the Niho-type decimation $d=3(p^m-1)+1$ over $\mathrm{GF}(p^{2m})$ for any prime $p \ge 5$. Previously th…
View article: On the parameters of extended primitive cyclic codes and the related designs
On the parameters of extended primitive cyclic codes and the related designs Open
Very recently, Heng et al. studied a family of extended primitive cyclic codes. It was shown that the supports of all codewords with any fixed nonzero Hamming weight of this code supporting 2-designs. In this paper, we study this family of…
View article: Several classes of 0-APN power functions over $\mathbb{F}_{2^n}$
Several classes of 0-APN power functions over $\mathbb{F}_{2^n}$ Open
Recently, the investigation of Partially APN functions has attracted a lot of attention. In this paper, with the help of resultant elimination and MAGMA, we propose several new infinite classes of 0-APN power functions over $\mathbb{F}_{2^…
View article: The $c$-differential spectrum of $x\mapsto x^{\frac{p^n+1}{2}}$ in finite fields of odd characteristics
The $c$-differential spectrum of $x\mapsto x^{\frac{p^n+1}{2}}$ in finite fields of odd characteristics Open
In the paper, we concentrate on the map $x\mapsto x^{\frac{p^n+1}{2}}$ on $\mathbb{F}_{p^n}$ and using combinatorial and number theory techniques, we compute its detailed $c$-differential spectrum for all values of $c\neq 1$ (the spectrum …
View article: Two Classes of Power Mappings with Boomerang Uniformity 2
Two Classes of Power Mappings with Boomerang Uniformity 2 Open
Let $q$ be an odd prime power. Let $F_1(x)=x^{d_1}$ and $F_2(x)=x^{d_2}$ be power mappings over $\mathrm{GF}(q^2)$, where $d_1=q-1$ and $d_2=d_1+\frac{q^2-1}{2}=\frac{(q-1)(q+3)}{2}$. In this paper, we study the the boomerang uniformity of…
View article: Two classes of power mappings with boomerang uniformity 2
Two classes of power mappings with boomerang uniformity 2 Open
Let be an odd prime power. Let and be power mappings over , where and . In this paper, we study the boomerang uniformity of and via their differential properties. It is shown that the boomerang uniformity of () is 2 with some condit…
View article: Differential spectra of a class of power permutations with Niho exponents
Differential spectra of a class of power permutations with Niho exponents Open
Let be a positive integer and . Let be a power permutation over , which is a monomial with a Niho exponent. In this paper, the differential spectrum of is investigated. It is shown that the differential spectrum of is when is even, a…
View article: The Differential Spectrum of the Power Mapping $x^{p^n-3}$
The Differential Spectrum of the Power Mapping $x^{p^n-3}$ Open
Let $n$ be a positive integer and $p$ a prime. The power mapping $x^{p^n-3}$ over $\mathbb{F}_{p^n}$ has desirable differential properties, and its differential spectra for $p=2,\,3$ have been determined. In this paper, for any odd prime $…
View article: Investigations on <i>c</i>-(Almost) Perfect Nonlinear Functions
Investigations on <i>c</i>-(Almost) Perfect Nonlinear Functions Open
In a prior paper \\cite{EFRST20}, two of us, along with P. Ellingsen, P. Felke\nand A. Tkachenko, 1defined a new (output) multiplicative differential, and the\ncorresponding $c$-differential uniformity, which has the potential of extending…
View article: On $-1$-differential uniformity of ternary APN power functions
On $-1$-differential uniformity of ternary APN power functions Open
Very recently, a new concept called multiplicative differential and the corresponding $c$-differential uniformity were introduced by Ellingsen et al. A function $F(x)$ over finite field $\mathrm{GF}(p^n)$ to itself is called $c$-differenti…
View article: Power Functions over Finite Fields with Low $c$-Differential Uniformity
Power Functions over Finite Fields with Low $c$-Differential Uniformity Open
Very recently, a new concept called multiplicative differential (and the corresponding $c$-differential uniformity) was introduced by Ellingsen \textit{et al} in [C-differentials, multiplicative uniformity and (almost) perfect c-nonlineari…
View article: New Ternary Power Mapping with Differential Uniformity Δ<i><sub>f</sub></i>≤3 and Related Optimal Cyclic Codes
New Ternary Power Mapping with Differential Uniformity Δ<i><sub>f</sub></i>≤3 and Related Optimal Cyclic Codes Open
In this letter, the differential uniformity of power function f(x)=xe over GF(3m) is studied, where m≥3 is an odd integer and $e=\frac{3^m-3}{4}$. It is shown that Δf≤3 and the power function is not CCZ-equivalent to the known ones. Moreov…
View article: On an open problem about a class of optimal ternary cyclic codes
On an open problem about a class of optimal ternary cyclic codes Open
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In this paper, we settle an open problem abo…
View article: Parameters of LCD BCH codes with two lengths
Parameters of LCD BCH codes with two lengths Open
In this paper, we study LCD BCH codes over the finite field GF$(q)$ with two types of lengths $n$, where $n = q^l+1$ and $n = (q^l+1)/(q+1)$. Several classes of LCD BCH codes are given and their parameters are determined or bounded by expl…