7 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…