Liqin Qian

activity

20162023

Z_{4} [u] / ⟨ u^{2} - 1 ⟩

and their Gray images

65 citations · 126 across the 10 of their papers we have counts for

collaborators

10 papers

math.NT2023

A new method for solving the equation $x^{d} + (x + 1)^{d} = b$ in $F_{q^{4}}$ where $d = q^{3} + q^{2} + q - 1$

Liqin Qian, Minjia Shi, Wei Lu

In this paper, we give a new method answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski about the equation $x^{d} + (x + 1)^{d} = b$ in $\mathbb{F}_…

cs.IT2021

A new method for constructing linear codes with small hulls

Liqin Qian, Xiwang Cao, Wei Lu +1

The hull of a linear code over finite fields is the intersection of the code and its dual, which was introduced by Assmus and Key. In this paper, we develop a method to construct l…

cs.IT2019

New constructions of asymptotically optimal codebooks via character sums over a local ring

Liqin Qian, Xiwang Cao, Wei Lu +1

In this paper, we present explicit description on the additive characters, multiplicative characters and Gauss sums over a local ring. As an application, based on the additive char…

cs.IT2018★ 6 cited

On self-dual and LCD double circulant and double negacirculant codes over $F_{q} + u F_{q}$

Minjia Shi, Hongwei Zhu, Liqin Qian +2

Double circulant codes of length $2 n$ over the semilocal ring $R = F_{q} + u F_{q}, u^{2} = u,$ are studied when $q$ is an odd prime power, and $- 1$ is a square in $\mat…

cs.IT2018

Linear codes with few weights over $F_{2} + u F_{2}$

Minjia Shi, Liqin Qian, Patrick Sole

In this paper, we construct an infinite family of five-weight codes from trace codes over the ring $R = F_{2} + u F_{2}$ , where $u^{2} = 0.$ The trace codes have the algebraic…

cs.IT2017★ 55 cited

On self-dual negacirculant codes of index two and four

Minjia Shi, Qian Liqin, Patrick Sole

In this paper, we study a special kind of factorization of $x^{n} + 1$ over $F_{q},$ with $q$ a prime power $\equiv 3 (mod 4)$ when $n = 2 p,$ with $p \equiv 3 (mod 4)$ …

cs.IT2017

New Classes of $p$ -ary Few Weights Codes

Minjia Shi, Rongsheng Wu, Liqin Qian +2

In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring $R=\mathbb{F}_p+u\mathbb{F}_p+\cdots +u^{k-1}\mathbb{F}_{p}…

cs.IT2016

New few weight codes from trace codes over a local Ring

Shi Minjia, Qian Liqin, Sole Patrick

In this paper, new few weights linear codes over the local ring $R = F_{p} + u F_{p} + v F_{p} + uv F_{p},$ with $u^{2} = v^{2} = 0, uv = v u,$ are constructed by using the t…

cs.IT2016★ 65 cited

On constacyclic codes over $Z_{4} [u] / ⟨ u^{2} - 1 ⟩$ and their Gray images

Minjia Shi, Liqing Qian, Lin Sok +2

We first define a new Gray map from $R = Z_{4} + u Z_{4}$ to $Z_{4}^{2}$ , where $u^{2} = 1$ and study $(1 + 2 u)$ -constacyclic codes over $R$ . Also of interest are some…

cs.IT2016

Good Self-dual Generalized Quasi-Cyclic Codes Exist

MinJia Shi, Yan Liu, Patrick Solé

We show that there are good long binary generalized quasi-cyclic self-dual (either Type I or Type II) codes.

A new method for solving the equation xd+(x+1)d=b in Fq4​ where d=q3+q2+q−1