Zobrazeno 1 - 10
of 599
pro vyhledávání: '"Zhu Shixin"'
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 abelian groups and cyclic groups and use these groups to construct linear
Externí odkaz:
http://arxiv.org/abs/2412.15551
Autor:
Wan, Ruhao, Zhu, Shixin
Let $q=p^m$ be a prime power, $e$ be an integer with $0\leq e\leq m-1$ and $s=\gcd(e,m)$. In this paper, for a vector $v$ and a $q$-ary linear code $C$, we give some necessary and sufficient conditions for the equivalent code $vC$ of $C$ and the exte
Externí odkaz:
http://arxiv.org/abs/2412.05011
Autor:
Zhi, Yujie, Zhu, Shixin
Maximum distance separable (MDS) and near maximum distance separable (NMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes due to their algebraic properties and excellent error-correcting
Externí odkaz:
http://arxiv.org/abs/2406.03693
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 {general} dual-containing matrix-product code; the second one is founded o
Externí odkaz:
http://arxiv.org/abs/2405.06292
Binary cyclic codes have been a hot topic for many years, and significant progress has been made in the study of this types of codes. As is well known, it is hard to construct infinite families of binary cyclic codes [n, n+1/2] with good minimum dist
Externí odkaz:
http://arxiv.org/abs/2404.18053
Autor:
Wan, Ruhao, Zhu, Shixin
In this paper, we study the Hermitian hulls of generalized Reed-Solomon (GRS) codes over finite fields. For a given class of GRS codes, by extending the length, increasing the dimension, and extending the length and increasing the dimension at the sa
Externí odkaz:
http://arxiv.org/abs/2401.08195
Autor:
Li, Yang, Zhu, Shixin
In this paper, we study a class of special linear codes involving their parameters, weight distributions, self-orthogonal properties, deep holes, and the existence of error-correcting pairs. We prove that such codes must be maximum distance separable
Externí odkaz:
http://arxiv.org/abs/2401.04360
In order to correct the pair-errors generated during the transmission of modern high-density data storage that the outputs of the channels consist of overlapping pairs of symbols, a new coding scheme named symbol-pair code is proposed. The error-corr
Externí odkaz:
http://arxiv.org/abs/2401.01619
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 linear complementary dual (LCD) codes and quantum codes. In this paper
Externí odkaz:
http://arxiv.org/abs/2312.04261
Cyclic codes are an interesting family of linear codes since they have efficient decoding algorithms and contain optimal codes as subfamilies. Constructing infinite families of cyclic codes with good parameters is important in both theory and practic
Externí odkaz:
http://arxiv.org/abs/2310.20179