13 papers
New record-breaking binary linear codes constructed from group codes
Cong Yu, Shixin Zhu, Hao Chen +2
In this paper, we employ group rings and automorphism groups of binary linear codes to construct new record-breaking binary linear codes. We consider the semidirect product of abel…
On general self-orthogonal matrix-product codes associated with Toeplitz matrices
Yang Li, Shixin Zhu, Edgar Martínez-Moro
In this paper, we present four constructions of {general} self-orthogonal matrix-product codes associated with Toeplitz matrices. The first one relies on the {dual} of a known {gen…
A family of linear codes that are either non-GRS MDS codes or NMDS codes
Yang Li, Zhonghua Sun, Shixin Zhu
Both maximum distance separable (MDS) codes that are not equivalent to generalized Reed-Solomon (GRS) codes (non-GRS MDS codes) and near MDS (NMDS) codes have nice applications in…
New ternary self-orthogonal codes and related LCD codes from weakly regular plateaued functions
Dengcheng Xie, Shixin Zhu, Yang Li
A linear code is said to be self-orthogonal if it is contained in its dual. Self-orthogonal codes are of interest because of their important applications, such as for constructing…
On -MDS codes and a conjecture on infinite families of -MDS codes
Yang Li, Shixin Zhu, Edgar Martínez-Moro
The class of -maximum distance separable (-MDS) codes {is a} generalization of maximum distance separable (MDS) codes {that} has attracted a lot of attention due to its…
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…
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…
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…
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…