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Publications (25)

cs.IT2020

Power Functions over Finite Fields with Low $c$ -Differential Uniformity

Haode Yan, Sihem Mesnager, Zhengchun Zhou

Very recently, a new concept called multiplicative differential (and the corresponding $c$ -differential uniformity) was introduced by Ellingsen \textit{et al} in [C-differentials,…

cs.IT2025

A note on the differential spectrum of a class of locally APN functions

Haode Yan, Ketong Ren

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 $f_{u} (x) = x^{\frac{p ^{n} + 3}{2}} + u x^{2}$ over $\gf_{p^n…

math.NT2013

Incidence Matrices of Polarized Projective Spaces

Chunlei Liu, Haode Yan

In this paper, we first define a non-degenerate symmetric bilinear form on Fq^4. Then we get an incidence matrix G of Fq^4 by the bilinear form. By its corresponding quadratic form…

cs.IT2026

A class of locally differentially $4$ -uniform power functions with Niho exponents

Haode Yan, Kangquan Li

Niho exponents have found important applications in sequence design, coding theory, and cryptography. Determining the differential spectrum of a power function with Niho exponent i…

cs.IT2025

On the Hamming Weight Functions of Linear Codes

Dongmei Huang, Qunying Liao, Sihem Mesnager +2

Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary…

cs.IT2022

Two Classes of Power Mappings with Boomerang Uniformity 2

Zhen Li, Haode Yan

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 $GF (q^{2})$ , where $d_{1} = q - 1$ and $d_2=d_1+\frac{q^2-1}{2}=\frac{(q-1)(q+3)}{2…

cs.CR2022

Boomerang Spectra of Two Classes of Power Functions via Their Differential Spectra

Ziying Zhang, Haode Yan, Zhen Li

In EUROCRYPT 2018, Cid $e t a l .$ introduced a new concept on the cryptographic property of S-boxes to evaluate the subtleties of boomerang-style attacks. This concept was named as…

cs.IT2023

On correlation distribution of Niho-type decimation $d = 3 (p^{m} - 1) + 1$

Maosheng Xiong, Haode Yan

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 $…

cs.IT2023

Codes and Pseudo-Geometric Designs from the Ternary $m$ -Sequences with Welch-type decimation $d = 2 \cdot 3^{(n - 1) /2} + 1$

Can Xiang, Chunming Tang, Haode Yan +1

Pseudo-geometric designs are combinatorial designs which share the same parameters as a finite geometry design, but which are not isomorphic to that design. As far as we know, many…

cs.IT2021

On $- 1$ -differential uniformity of ternary APN power functions

Haode Yan

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…

cs.IT2023

Subfield Codes of Several Few-Weight Linear Codes Parametrized by Functions and Their Consequences

Li Xu, Cuiling Fan, Sihem Mesnager +2

Subfield codes of linear codes over finite fields have recently received much attention. Some of these codes are optimal and have applications in secrete sharing, authentication co…

cs.IT2021

Investigations on $c$ -(almost) perfect nonlinear functions

Sihem Mesnager, Constanza Riera, Pantelimon Stanica +2

In a prior paper \cite{EFRST20}, two of us, along with P. Ellingsen, P. Felke and A. Tkachenko, 1defined a new (output) multiplicative differential, and the corresponding $c$ -diffe…

cs.CR2024

A note on the differential spectrum of the Ness-Helleseth function

Ketong Ren, Maosheng Xiong, Haode Yan

Let $n ⩾ 3$ be an odd integer and $u$ an element in the finite field $\gf_{3^n}$. The Ness-Helleseth function is the binomial $f_{u} (x) = u x^{d_{1}} + x^{d_{2}}$ over $\gf_{3^n}$, wher…

cs.IT2022

On the differential spectrum of a class of APN power functions over odd characteristic finite fields and their $c$ -differential properties

Haode Yan, Sihem Mesnager, Xiantong Tan

Only three classes of Almost Perfect Nonlinear (for short, APN) power functions over odd characteristic finite fields have been investigated in the literature, and their differenti…

math.CO2019

On an open problem about a class of optimal ternary cyclic codes

Dongchun Han, Haode Yan

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 decodi…

cs.IT2021

The Differential Spectrum of the Power Mapping $x^{p^{n} - 3}$

Haode Yan, Yongbo Xia, Chunlei Li +3

Let $n$ be a positive integer and $p$ a prime. The power mapping $x^{p^{n} - 3}$ over $F_{p^{n}}$ has desirable differential properties, and its differential spectra for $p=2,\,…

cs.IT2015

Higher weight distribution of linearized Reed-Solomon codes

Haode Yan, Yan Liu, Chunlei Liu

Linearized Reed-Solomon codes are defined. Higher weight distribution of those codes are determined.

math.NT2013

A Class of Six-weight Cyclic Codes and Their Weight Distribution

Yan Liu, Haode Yan, Chunlei Liu

In this paper, a family of six-weight cyclic codes over GF(p) whose duals have two zeros is presented, where p is an odd prime. And the weight distribution of these cyclic codes is…

cs.IT2015

Linearized Reed-Solomon codes and linearized Wenger graphs

Haode Yan, Chunlei Liu

A codeword is associated to a linearized polynomial. The weight distribution of the codewords is determined as the linearized polynomial varies in a family of fixed degree. There i…

cs.IT2015

A Class of Five-weight Cyclic Codes and Their Weight Distribution

Yan Liu, Haode Yan

In this paper, a family of five-weight reducible cyclic codes is presented. Furthermore, the weight distribution of these cyclic codes is determined, which follows from the determi…

math.NT2025

On covering radius of generalized Zetterberg codes

Haode Yan, Maosheng Xiong

We employ analytic number theoretic techniques, specifically character sums and Weil type estimates, to study the covering radius of the generalized Zetterberg codes over all finit…

cs.IT2022

The $c$ -differential spectrum of $x \mapsto x^{\frac{p ^{n} + 1}{2}}$ in finite fields of odd characteristics

Constanza Riera, Pantelimon Stanica, Haode Yan

In the paper, we concentrate on the map $x \mapsto x^{\frac{p ^{n} + 1}{2}}$ on $F_{p^{n}}$ and using combinatorial and number theory techniques, we compute its detailed $c$ -diffe…

cs.IT2022

Two low differentially uniform power permutations over odd characteristic finite fields: APN and differentially $4$ -uniform functions

Haode Yan, Sihem Mesnager, Xiantong Tan

Permutation polynomials over finite fields are fundamental objects as they are used in various theoretical and practical applications in cryptography, coding theory, combinatorial…

cs.IT2022

Several classes of 0-APN power functions over $F_{2^{n}}$

Tao Fu, Haode Yan

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 inf…

cs.IT2023

On the parameters of extended primitive cyclic codes and the related designs

Haode Yan, Yanan Yin

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 s…

Publications (25)

Power Functions over Finite Fields with Low c-Differential Uniformity

A note on the differential spectrum of a class of locally APN functions

Incidence Matrices of Polarized Projective Spaces

A class of locally differentially 4-uniform power functions with Niho exponents

On the Hamming Weight Functions of Linear Codes

Two Classes of Power Mappings with Boomerang Uniformity 2

Boomerang Spectra of Two Classes of Power Functions via Their Differential Spectra

On correlation distribution of Niho-type decimation d=3(pm−1)+1

Codes and Pseudo-Geometric Designs from the Ternary m-Sequences with Welch-type decimation d=2⋅3(n−1)/2+1

On −1-differential uniformity of ternary APN power functions

Subfield Codes of Several Few-Weight Linear Codes Parametrized by Functions and Their Consequences

Investigations on c-(almost) perfect nonlinear functions

A note on the differential spectrum of the Ness-Helleseth function

On the differential spectrum of a class of APN power functions over odd characteristic finite fields and their c-differential properties

On an open problem about a class of optimal ternary cyclic codes

The Differential Spectrum of the Power Mapping xpn−3

Higher weight distribution of linearized Reed-Solomon codes

A Class of Six-weight Cyclic Codes and Their Weight Distribution

Linearized Reed-Solomon codes and linearized Wenger graphs

A Class of Five-weight Cyclic Codes and Their Weight Distribution

On covering radius of generalized Zetterberg codes

The c-differential spectrum of x↦x2pn+1​ in finite fields of odd characteristics

Two low differentially uniform power permutations over odd characteristic finite fields: APN and differentially 4-uniform functions

Several classes of 0-APN power functions over F2n​

On the parameters of extended primitive cyclic codes and the related designs

Power Functions over Finite Fields with Low $c$ -Differential Uniformity

A class of locally differentially $4$ -uniform power functions with Niho exponents

On correlation distribution of Niho-type decimation $d = 3 (p^{m} - 1) + 1$

Codes and Pseudo-Geometric Designs from the Ternary $m$ -Sequences with Welch-type decimation $d = 2 \cdot 3^{(n - 1) /2} + 1$

On $- 1$ -differential uniformity of ternary APN power functions

Investigations on $c$ -(almost) perfect nonlinear functions

On the differential spectrum of a class of APN power functions over odd characteristic finite fields and their $c$ -differential properties

The Differential Spectrum of the Power Mapping $x^{p^{n} - 3}$

The $c$ -differential spectrum of $x \mapsto x^{\frac{p ^{n} + 1}{2}}$ in finite fields of odd characteristics

Two low differentially uniform power permutations over odd characteristic finite fields: APN and differentially $4$ -uniform functions

Several classes of 0-APN power functions over $F_{2^{n}}$