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Weiqiong Wang

Publications and source records attributed to Weiqiong Wang.

6 recordsLinked to original sources
arXiv2021

Linear complexity over ${\mathbb{F}_{q}}$ and 2-adic complexity of a class of binary generalized cyclotomic sequences with low-value autocorrelation

A class of binary sequences with period $2p$ is constructed using generalized cyclotomic classes, and their linear complexity, minimal polynomial over ${\mathbb{F}_{q}}$ as well as 2-adic complexity are determined using Gauss period and group ring theory. The results show that the linear complexity of these sequences attains the maximum when $p\equiv \pm 1(\bmod~8)$ and is equal to {$p$+1} when $p\equiv \pm 3(\bmod~8)$ over extension field. Moreover, the 2-adic complexity of these sequences is maximum. According to Berlekamp-Massey(B-M) algorithm and the rational approximation algorithm(RAA), these sequences have quite good cryptographyic properties in the aspect of linear complexity and 2-adic complexity.

cs.IT↗
arXiv2020

Optimal Binary Linear Codes from Maximal Arcs

The binary Hamming codes with parameters $[2^m-1, 2^m-1-m, 3]$ are perfect. Their extended codes have parameters $[2^m, 2^m-1-m, 4]$ and are distance-optimal. The first objective of this paper is to construct a class of binary linear codes with parameters $[2^{m+s}+2^s-2^m,2^{m+s}+2^s-2^m-2m-2,4]$, which have better information rates than the class of extended binary Hamming codes, and are also distance-optimal. The second objective is to construct a class of distance-optimal binary codes with parameters $[2^m+2, 2^m-2m, 6]$. Both classes of binary linear codes have new parameters.

cs.IT↗
arXiv2019

The parameters of a family of linear codes

A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the sense that they meet certain bounds on linear codes. Applications of these codes in secret sharing schemes and combinational designs are presented.

cs.IT↗
arXiv2017

On jumped Wenger graphs

In this paper we introduce a new infinite class of bipartite graphs, called jumped Wenger graphs, which are closely related to Wenger graphs. An tight upper bound of the diameter and the exact girth of a jumped Wenger graph $J_m(q, i, j )$ for integers $i, j$, $1\leq i <j \leq m+2$, are determined. In particular, the exact diameter of the jumped Wenger graph $J_m(q, i, j)$ if $(i, j)=(m,m+2), (m+1,m+2)$ or $(m,m+1)$ is also obtained.

math.CO↗
arXiv2017

Counting Polynomials with Distinct Zeros in Finite Fields

Let $\mathbb{F}_q$ be a finite field with $q=p^e$ elements, where $p$ is a prime and $e\geq 1$ is an integer. Let $\ell<n$ be two positive integers. Fix a monic polynomial $u(x)=x^n +u_{n-1}x^{n-1}+\cdots +u_{\ell+1}x^{\ell+1} \in \mathbb{F}_q[x]$ of degree $n$ and consider all degree $n$ monic polynomials of the form $$f(x) = u(x) + v_\ell(x), \ v_\ell(x)=a_\ell x^\ell+a_{\ell-1}x^{\ell-1}+\cdots+a_1x+a_0\in \mathbb{F}_q[x].$$ For integer $0\leq k \leq {\rm min}\{n,q\}$, let $N_k(u(x),\ell)$ denote the total number of $v_\ell(x)$ such that $u(x)+v_\ell(x)$ has exactly $k$ distinct roots in $\mathbb{F}_q$, i.e. $$N_k(u(x),\ell)=|\{f(x)=u(x)+v_l(x)\ |\ f(x)\ {\rm has\ exactly}\ k\ {\rm distinct\ zeros\ in}\ \mathbb{F}_q\}|.$$ In this paper, we obtain explicit combinatorial formulae for $N_k(u(x),\ell)$ when $n-\ell$ is small, namely when $n-\ell= 1, 2, 3$. As an application, we define two kinds of Wenger graphs called jumped Wenger graphs and obtain their explicit spectrum.

math.NT↗