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In this paper, based on the theory of defining sets, a class of four-weight or five-weight linear codes over Fp is constructed. The complete weight enumerators of the linear codes are determined by means of Weil sums. In some case, there is…

Information Theory · Computer Science 2020-12-10 Xina Zhang

We construct a family of two-Lee-weight codes over the ring $R_k,$ which is defined as trace codes with algebraic structure of abelian codes. The Lee weight distribution of the two-weight codes is given. Taking the Gray map, we obtain…

Information Theory · Computer Science 2016-12-19 Minjia Shi , Yue Guan

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

In this paper, for any odd prime $p$ and an integer $m\ge 3$, several classes of linear codes with $t$-weight $(t=3,5,7)$ are obtained based on some defining sets, and then their complete weight enumerators are determined explicitly by…

Information Theory · Computer Science 2022-08-30 Canze Zhu , Qunying Liao

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

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 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

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

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

Few-weight codes have been constructed and studied for many years, since their fascinating relations to finite geometries, strongly regular graphs and Boolean functions. Simplex codes are one-weight Griesmer $[\frac{q^k-1}{q-1},k…

Information Theory · Computer Science 2024-08-20 Xu Pan , Hao Chen , Hongwei Liu , Shengwei Liu

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

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

We construct an infinite family of two-Lee-weight and three-Lee-weight codes over the chain ring $\mathbb{F}_p+u\mathbb{F}_p.$ They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss…

Information Theory · Computer Science 2017-01-05 Minjia Shi , Yan Liu , Patrick Solé

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

We discuss a class of binary cyclic codes and their dual codes. The minimum distance is determined using algebraic geometry, and an application of Weil's theorem. We relate the weights appearing in the dual codes to the number of rational…

Number Theory · Mathematics 2007-05-23 Gary McGuire , Jose Felipe Voloch

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

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

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

The duals of cyclic codes with two zeros have been extensively studied, and their weight distributions have recently been evaluated in some cases. In this note, we determine the weight distribution of a certain new class of such codes by…

Combinatorics · Mathematics 2012-06-18 Tao Feng , Koji Momihara

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

Information Theory · Computer Science 2016-02-05 Chunming Tang , Can Xiang , Keqin Feng