94 citations · 152 across the 33 of their papers we have counts for
33 papers
Symplectic self-orthogonal and LCD codes from the Plotkin sum construction
Shixin Zhu, Yang Li, Shitao Li
In this work, we propose two criteria for linear codes obtained from the Plotkin sum construction being symplectic self-orthogonal (SO) and linear complementary dual (LCD). As spec…
Binomial pmf among arithmetic progressions and sieved sets in random walks
Jun Hong, Xiaosheng Wu, Shixin Zhu
We consider the distribution of the binomial probability mass function (pmf) among arithmetic progressions and obtain an average-type theorem. As applications, we consider the poss…
New entanglement-assisted quantum codes from negacyclic codes
Xiaojing Chen, Xingbo Lu, Shixin Zhu +2
The theory of entanglement-assisted quantum error-correcting codes (EAQECCs) is a generalization of the standard stabilizer quantum error-correcting codes, which can be possibly co…
New Quantum MDS codes from Hermitian self-orthogonal generalized Reed-Solomon codes
Ruhao Wan, Shixin Zhu
Quantum maximum-distance-separable (MDS for short) codes are an important class of quantum codes. In this paper, by using Hermitian self-orthogonal generalized Reed-Solomon (GRS fo…
The hull of two classical propagation rules and their applications
Yang Li, Shixin Zhu, Edgar Martínez-Moro
In this work, we study and determine the dimensions of Euclidean and Hermitian hulls of two classical propagation rules, namely, the direct sum construction and the $(\mathbf{u},\m…
On the Existence of Galois Self-Dual GRS and TGRS Codes
Shixin Zhu, Ruhao Wan
Let be a prime power and be an integer with . -Galois self-dual codes are generalizations of Euclidean and Hermitian ( with e…
Construction of MDS self-dual codes from generalized Reed-Solomon codes
Ruhao Wan, Shixin Zhu, Jin Li
MDS codes and self-dual codes are important families of classical codes in coding theory. It is of interest to investigate MDS self-dual codes. The existence of MDS self-dual codes…
Several classes of Galois self-orthogonal MDS codes and related applications
Yang Li, Yunfei Su, Shixin Zhu +2
Let be a prime power and be an integer with . -Galois self-orthogonal codes are generalizations of Euclidean self-orthogonal codes () and Hermi…
New MDS self-dual codes over finite fields $\F_{r^2}$
Ruhao Wan, Yang Li, Shixin Zhu
MDS self-dual codes have nice algebraic structures and are uniquely determined by lengths. Recently, the construction of MDS self-dual codes of new lengths has become an important…
On Galois hulls of linear codes and new entanglement-assisted quantum error-correcting codes
Yang Li, Shixin Zhu
The Galois hull of a linear code is the intersection of itself and its Galois dual code, which has aroused the interest of researchers in these years. In this paper, we study Galoi…
On MDS Codes With Galois Hulls of Arbitrary Dimensions
Yang Li, Shixin Zhu, Pi Li
The Galois hulls of linear codes are a generalization of the Euclidean and Hermitian hulls of linear codes. In this paper, we study the Galois hulls of (extended) GRS codes and pre…
MDS Codes with Euclidean and Hermitian Hulls of Flexible Dimensions and Their Applications to EAQECCs
Yang Li, Ruhao Wan, Shixin Zhu
The hull of a linear code is the intersection of itself with its dual code with respect to certain inner product. Both Euclidean and Hermitian hulls are of theorical and practical…
Cyclic codes and some new entanglement-assisted quantum MDS codes
Wan Jiang, Shixin Zhu, Xiaojing Chen
Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in protecting quantum information from decoherence and quantum noise. Recently, constructing…
On the constructions of -cycle permutations
Yuting Chen, Liqi Wang, Shixin Zhu
Any permutation polynomial is an -cycle permutation. When is a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle pe…
New entanglement-assisted quantum MDS codes with length
Shixin Zhu, Wan Jiang, Xiaojing Chen
The entanglement-assisted stabilizer formalism can transform arbitrary classical linear codes into entanglement-assisted quantum error correcting codes (EAQECCs). In this work, we…
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…
Euclidean and Hermitian Hulls of MDS Codes and Their Applications to EAQECCs
Weijun Fang, Fang-Wei Fu, Lanqiang Li +1
In this paper, we construct several classes of maximum distance separable (MDS) codes via generalized Reed-Solomon (GRS) codes and extended GRS codes, where we can determine the di…
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…
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…
A family of constacyclic codes over and its application to quantum codes
Yongsheng Tang, Ting Yao, Shixin Zhu +1
We introduce a Gray map from to and study -constacyclic codes over w…
A note on complete classification of -constacyclic codes of length over $\F_{p^m}+u\F_{p^m}+u^2\F_{p^m}$
Reza Sobhani, Zhonghua Sun, Liqi Wang +1
For units and in $\F_{p^m}$, the structure of -constacyclic codes of length over is studied and sel…
Several classes of optimal ternary cyclic codes
Lanqiang Li, Li Liu, Shixin Zhu
Cyclic codes have efficient encoding and decoding algorithms over finite fields, so that they have practical applications in communication systems, consumer electronics and data st…
The reversible negacyclic codes over finite fields
Shixin Zhu, Binbin Pang, Zhonghua Sun
In this paper, by investigating the factor of the , we deduce that the structure of the reversible negacyclic code over the finite field , where is an od…
One-Lee weight and two-Lee weight -additive codes
Zhenliang Lu, Liqi Wang, Shixin Zhu +1
In this paper, we study one-Lee weight and two-Lee weight codes over , where . Some properties of one-Lee weight $\mathbb{Z}_{2}\mathbb{Z}…