English
Related papers

Related papers: A family of linear codes with three weights

200 papers

Three classes of binary linear codes with at most four nonzero weights were constructed in this paper, in which two of them are projective three-weight codes. As applications, $s$-sum sets for any odd $ s > 1$ were constructed.

Information Theory · Computer Science 2025-08-26 Tonghui Zhang , Pinhui Ke , Zuling Chang

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

For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight…

Information Theory · Computer Science 2016-02-03 Fei Li , Yang Yan , Qiuyan Wang , Tongjiang Yan

A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…

Information Theory · Computer Science 2015-12-23 Can Xiang

Recently, linear codes constructed from defining sets have been investigated extensively and they have many applications. In this paper, for an odd prime $p$, we propose a class of $p$-ary linear codes by choosing a proper defining set.…

Information Theory · Computer Science 2017-07-07 Shudi Yang , Zheng-An Yao , Chang-An Zhao

We construct a class of linear codes by choosing a proper defining set and determine their complete weight enumerators and weight enumerators. The results show that they are at most three-weight codes and they are suitable for applications…

Information Theory · Computer Science 2019-01-23 Shudi Yang , Xiangli Kong

Linear codes have been an interesting subject of study for many years, as linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a class of…

Information Theory · Computer Science 2016-01-27 Can Xiang , Chunming Tang , Keqin Feng

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

Boolean functions have very nice applications in cryptography and coding theory, which have led to a lot of research focusing on their applications. The objective of this paper is to construct binary linear codes with few weights from the…

Information Theory · Computer Science 2020-06-18 Xiaoqiang Wang , Dabin Zheng , Yan Zhang

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

In this article we present a class of codes with few weights arising from special type of linear sets. We explicitly show the weights of such codes, their weight enumerator and possible choices for their generator matrices. In particular,…

Combinatorics · Mathematics 2020-05-07 Vito Napolitano , Ferdinando Zullo

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime $p$, we present the explicit complete weight enumerator of a family of $p$-ary linear codes constructed with defining…

Information Theory · Computer Science 2017-07-07 Shudi Yang , Zheng-An Yao

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

We provide a combinatorial construction for linear codes attaining the maximum possible number of distinct weights. We then introduce the related problem of determining the existence of linear codes with an arbitrary number of distinct…

Combinatorics · Mathematics 2018-04-20 Alessio Meneghetti

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 this paper, we construct an infinite family of three-weight binary codes from linear codes over the ring $R=\mathbb{F}_2+v\mathbb{F}_2+v^2\mathbb{F}_2$, where $v^3=1.$ These codes are defined as trace codes. They have the algebraic…

Information Theory · Computer Science 2018-07-03 Minjia Shi , Hongwei Zhu , Patrick Solé

Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of $p$-ary linear codes with two or three weights are constructed…

Information Theory · Computer Science 2015-10-20 Zhengchun Zhou , Nian Li , Cuiling Fan , Tor Helleseth

Based on a generic construction, two classes of ternary three-weight linear codes are obtained from a family of power functions, including some APN power functions. The weight distributions of these linear codes are determined through…

Information Theory · Computer Science 2016-04-12 Yongbo Xia , Chunlei Li

A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…

Information Theory · Computer Science 2019-03-20 Weiqiong Wang , Yan Wang

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
‹ Prev 1 2 3 10 Next ›