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In this manuscript, we construct a class of projective three-weight linear codes and two classes of projective four-weight linear codes over F2 from the defining sets construction, and determine their weight distributions by using additive…

Information Theory · Computer Science 2025-11-04 Qunying Liao , Zhaohui Zhang , Peipei Zheng

The linear codes with a few weights have been applied widely in combinatorial designs, secret sharing, association schemes, authentication codes and strongly regular graphs. In this paper, we first correct an erroneous result about the…

Information Theory · Computer Science 2020-09-21 Fei Li , Xiumei Li

Linear codes with a few weights have been widely investigated in recent years. In this paper, we mainly use Gauss sums to represent the Hamming weights of a class of $q$-ary linear codes under some certain conditions, where $q$ is a power…

Information Theory · Computer Science 2016-05-12 Ziling Heng , Qin Yue

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

In this paper, based on the theory of defining sets, two classes of five-weight or six-weight linear codes over Fp are constructed. The weight distributions of the linear codes are determined by means of Weil sums and a new type of…

Information Theory · Computer Science 2021-04-09 Xina Zhang

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

The determination of the weight distribution of linear codes has been a fascinating problem since the very beginning of coding theory. There has been a lot of research on weight enumerators of special cases, such as self-dual codes and…

Combinatorics · Mathematics 2021-09-28 Alessio Meneghetti , Marco Pellegrini , Massimiliano Sala

In this paper, a class of two-weight and three-weight linear codes over $\gf(p)$ is constructed, and their application in secret sharing is investigated. Some of the linear codes obtained are optimal in the sense that they meet certain…

Information Theory · Computer Science 2015-03-24 Kelan Ding , Cunsheng Ding

Linear codes with few weights have been a significant area of research in coding theory for many years, due to their applications in secret sharing schemes, authentication codes, association schemes, and strongly regular graphs. Inspired by…

Information Theory · Computer Science 2025-10-30 Mrinal Kanti Bose , Abhay Kumar Singh

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

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

In this paper, based on the theory of defining sets, two classes of at most six-weight linear codes over $\mathbb{F}_p$ are constructed. The weight distributions of the linear codes are determined by means of Gaussian period and Weil sums.…

Information Theory · Computer Science 2024-12-19 Xina Zhang

Linear codes with few weights have applications in data storage systems, secret sharing schemes, and authentication codes. In this paper, some kinds of p-ary linear codes with few weights are constructed by use of the given de ning set,…

Information Theory · Computer Science 2024-07-16 Mengzhen Zhao , Yanxun Chang

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

Linear codes with a few weights are an important class of codes in coding theory and have attracted a lot of attention. In this paper, we present several constructions of $q$-ary linear codes with two or three weights from vectorial…

Information Theory · Computer Science 2022-07-26 Jiaxin Wang , Zexia Shi , Yadi Wei , Fang-Wei Fu

Linear codes with a few weights have important applications in authentication codes, secret sharing, consumer electronics, etc.. The determination of the parameters such as Hamming weight distributions and complete weight enumerators of…

Information Theory · Computer Science 2017-11-15 Minglong Qi , Shengwu Xiong , Jingling Yuan , Wenbi Rao , Luo Zhong

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 topic in both theory and practice for many years. In this paper, for an odd prime power $q$, we construct some class of linear code over finite field $\mathbb{F}_q$ with defining set be the preimage of…

Information Theory · Computer Science 2016-01-27 Xiaoni Du , Yunqi Wan

Determining the weight distribution of a linear code is a classical and fundamental topic in coding theory that has been extensively investigated. Repeated-root cyclic codes, which form a significant subclass of error-correcting codes, have…

Information Theory · Computer Science 2025-08-07 Wei Zhao , Weixian Li , Shenghao Yang , Fang-Wei Fu , Kenneth W. Shum

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