English
Related papers

Related papers: A class of linear codes with few weights

200 papers

Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of linear codes has many applications such as on the type II wire-tap channel, dealing with…

Information Theory · Computer Science 2021-06-08 Fei Li , Xiumei Li

In the past few years, linear codes with few weights and their weight analysis have been widely studied. In this paper, we further investigate a class of two-weight or three-weight linear codes from defining sets and determine their weight…

Information Theory · Computer Science 2020-09-11 Dabin Zheng , Qing Zhao , Xiaoqiang Wang , Yan Zhang

Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…

Information Theory · Computer Science 2015-08-17 Chunming Tang , Nian Li , Yanfeng Qi , Zhengchun Zhou , Tor Helleseth

Linear codes with few weights have applications in authentication codes, secrete sharing schemes, association schemes, consumer electronics and data storage system. In this paper, several classes of linear codes with two or three weights…

Information Theory · Computer Science 2020-07-23 Guangkui Xu , Xiwang Cao

The weight distribution and weight hierarchy of linear codes are two important research topics in coding theory. In this paper, by choosing proper defining sets from inhomogeneous quadratic functions over $\mathbb{F}_{q}^{2},$ we construct…

Information Theory · Computer Science 2022-06-17 Fei Li , Xiumei Li

Linear codes with few weights have significant applications in secret sharing schemes, authentication codes, association schemes, and strongly regular graphs. There are a number of methods to construct linear codes, one of which is based on…

Information Theory · Computer Science 2023-11-01 Yadi Wei , Jiaxin Wang , Fang-Wei Fu

The objective of this paper is to construct a class of linear codes with two nonzero weights and three nonzero weights by using the general trace functions, which weight distributions has been determined. These linear codes contain some…

Information Theory · Computer Science 2016-11-22 Li Liu , Xianhong Xie , Lanqiang Li

Linear codes have been an interesting subject of study for many years. Recently, linear codes with few weights have been constructed and extensively studied. In this paper, for an odd prime p, a class of three-weight linear codes over Fp…

Information Theory · Computer Science 2015-12-24 Qiuyan Wang , Fei Li , Dongdai Lin

It is well-known that few-weight linear codes have better applications in secret sharing schemes \cite{JY2006,CC2005}.In particular, projective two-weight codes are very precious as they are closely related to finite projective spaces,…

Information Theory · Computer Science 2022-11-10 Canze Zhu , Qunying Liao

A linear code of length $n$ over a finite chain ring $R$ with residue field $\F_q$ is a $R$-submodule of $R^n$. A $R$-linear code is a code over $\F_q$ (not necessarily linear) which is the generalized Gray map image of a linear code over…

Information Theory · Computer Science 2025-12-03 Cristina Fernández-Córdoba , Sergi Sánchez-Aragón , Mercè Villanueva

Linear codes with few weights have many applications in secret sharing schemes, authentication codes, communication and strongly regular graphs. In this paper, we consider linear codes with three weights in arbitrary characteristic. To do…

Information Theory · Computer Science 2017-03-27 Sihem Mesnager , Ferruh Özbudak , Ahmet Sınak

Cyclic codes with a few weights are very useful in the design of frequency hopping sequences and the development of secret sharing schemes. In this paper, we mainly use Gauss sums to represent the Hamming weights of a general construction…

Information Theory · Computer Science 2015-10-20 Ziling Heng , Qin Yue

Recently, linear codes constructed by defining sets have attracted a lot of study, and many optimal linear codes with a few weights have been produced. The objective of this paper is to present a class of binary linear codes with three…

Information Theory · Computer Science 2016-08-22 Yang Yan , Fei Li , Qiuyan Wang

Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…

Information Theory · Computer Science 2020-05-12 Ahmet Sınak

Linear codes with a few weights can be applied to secrete sharing, authentication codes, association schemes and strongly regular graphs. For an odd prime power $q$, we construct a class of three-weight $\F_q$-linear codes from quadratic…

Information Theory · Computer Science 2024-10-04 Xiumei Li , Zongxi Chen , Fei Li

Recently, some infinite families of binary minimal and optimal linear codes are constructed from simplicial complexes by Hyun {\em et al}. Inspired by their work, we present two new constructions of codes over the ring $\Bbb F_2+u\Bbb F_2$…

Information Theory · Computer Science 2019-10-11 Yansheng Wu , Xiaomeng Zhu , Qin Yue

In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…

Information Theory · Computer Science 2022-01-03 Yansheng Wu , Chengju Li , Fu Xiao

In this paper, new few weights linear codes over the local ring $R=\mathbb{F}_p+u\mathbb{F}_p+v\mathbb{F}_p+uv\mathbb{F}_p,$ with $u^2=v^2=0, uv=vu,$ are constructed by using the trace function defined over an extension ring of degree $m.$…

Information Theory · Computer Science 2016-12-15 Shi Minjia , Qian Liqin , Sole Patrick

Linear codes with a few weights have wide applications in information security, data storage systems, consuming electronics and communication systems. Construction of the linear codes with a few weights and determination of their parameters…

Information Theory · Computer Science 2019-01-18 Minglong Qi , Shengwu Xiong

Minimal linear codes have significant applications in secret sharing schemes and secure two-party computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many…

Information Theory · Computer Science 2018-08-14 Sihem Mesnager , Ahmet Sınak