X. Kai

activity

20162024

most citedSome new bounds on LCD codes over finite fields

18 citations · 23 across the 11 of their papers we have counts for

collaborators

11 papers

cs.IT2024

New quantum codes from constacyclic codes over finite chain rings

Yongsheng Tang, Ting Yao, Heqian Xu +1

Let $R$ be the finite chain ring $F_{p^{2 m}} + u F_{p^{2 m}}$ , where $F_{p^{2 m}}$ is the finite field with $p^{2 m}$ elements, $p$ is a prime, $m$ is a non-…

cs.IT2023

On Galois self-orthogonal algebraic geometry codes

Yun Ding, Shixin Zhu, Xiaoshan Kai +1

Galois self-orthogonal (SO) codes are generalizations of Euclidean and Hermitian SO codes. Algebraic geometry (AG) codes are the first known class of linear codes exceeding the Gil…

cs.IT2019★ 1 cited

A Class of Narrow-Sense BCH Codes

Shixin Zhu, Zhonghua Sun, Xiaoshan Kai

BCH codes are an important class of cyclic codes which have applications in satellite communications, DVDs, disk drives, and two-dimensional bar codes. Although BCH codes have been…

cs.IT2018★ 18 cited

Some new bounds on LCD codes over finite fields

Binbin Pang, Shixin Zhu, Xiaoshan Kai

In this paper, we show that LCD codes are not equivalent to linear codes over small finite fields. The enumeration of binary optimal LCD codes is obtained. We also get the exact va…

cs.IT2018

Entanglement-assisted quantum MDS codes constructed from constacyclic codes

Xiaojing Chen, Shixin Zhu, Xiaoshan Kai

Recently, entanglement-assisted quantum error correcting codes (EAQECCs) have been constructed by cyclic codes and negacyclic codes. In this paper, by analyzing the cyclotomic cose…

cs.IT2017

A family of constacyclic codes over $F_{2^{m}} + u F_{2^{m}}$ and its application to quantum codes

Yongsheng Tang, Ting Yao, Shixin Zhu +1

We introduce a Gray map from $F_{2^{m}} + u F_{2^{m}}$ to $F_{2}^{2 m}$ and study $(1 + u)$ -constacyclic codes over $F_{2^{m}} + u F_{2^{m}},$ w…

cs.IT2016★ 3 cited

On $Z_{2} Z_{2} [u]$ - $(1 + u)$ -additive constacyclic

Ping Li, Wei Dai, Xiaoshan Kai

In this paper, we study $Z_{2} Z_{2} [u]$ - $(1 + u)$ -additive constacyclic code of arbitrary length. Firstly, we study the algebraic structure of this family of codes…

math.RA2016

One-Lee weight and two-Lee weight $Z_{2} Z_{2} [u]$ -additive codes

Zhenliang Lu, Liqi Wang, Shixin Zhu +1

In this paper, we study one-Lee weight and two-Lee weight codes over $Z_{2} Z_{2} [u]$ , where $u^{2} = 0$ . Some properties of one-Lee weight $\mathbb{Z}_{2}\mathbb{Z}…

cs.IT2016

New quantum codes from dual-containing cyclic codes over finite rings

Yongsheng Tang, Shixin Zhu, Xiaoshan Kai +1

Let $R = F_{2^{m}} + u F_{2^{m}} + \dots + u^{k} F_{2^{m}}$ , where $F_{2^{m}}$ is a finite field with $2^{m}$ elements, $m$ is a positive integer, $u$ i…

cs.IT2016

MacWilliams type identities on the Lee and Euclidean weights for linear codes over $Z_{ℓ}$

Yongsheng Tang, Shixin Zhu, Xiaoshan Kai

Motivated by the works of Shiromoto [3] and Shi et al. [4], we study the existence of MacWilliams type identities with respect to Lee and Euclidean weight enumerators for linear co…

cs.IT2016★ 1 cited

Repeated-root constacyclic codes of length $3 l p^{s}$ and their dual codes

Li Liu, Lanqiang Li, Xiaoshan Kai +1

Let $p \neq = 3$ be any prime and $l \neq = 3$ be any odd prime with $g c d (p, l) = 1$ . $F_{q}^{*} = ⟨ ξ ⟩$ is decomposed into mutually disjoint union of $g c d (q - 1, 3 l p^{s})$ coset over t…