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Linear codes with a few weights have many nice applications including combinatorial design, distributed storage system, secret sharing schemes and so on. In this paper, we construct two families of linear codes with a few weights based on…

Information Theory · Computer Science 2022-10-12 Ziling Heng , Xinran Wang , Xiaoru Li

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

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 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

Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary…

Information Theory · Computer Science 2016-12-15 Deng Tang , Claude Carlet , Zhengchun Zhou

Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of $t$-weight linear codes over ${\mathbb F}_{q}$ are presented with…

Information Theory · Computer Science 2025-01-22 Zhao Hu , Mingxiu Qiu , Nian Li , Xiaohu Tang , Liwei Wu

A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the…

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

Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, secure two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then…

Information Theory · Computer Science 2022-01-11 Haibo Liu , Qunying Liao

Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then…

Information Theory · Computer Science 2021-11-23 Haibo Liu Qunying Liao , Canze Zhu

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

In this paper, we apply two-to-one functions over $\mathbb{F}_{2^n}$ in two generic constructions of binary linear codes. We consider two-to-one functions in two forms: (1) generalized quadratic functions; and (2) $\left(x^{2^t}+x\right)^e$…

Information Theory · Computer Science 2020-06-23 Kangquan Li , Chunlei Li , Tor Helleseth , Longjiang Qu

In this article, we present two new approaches to construct minimal linear codes of dimension $n+1$ over $\mathbb{F}_{3}$ using characteristic and ternary functions. We also obtain the weight distributions of these constructed minimal…

Information Theory · Computer Science 2024-05-24 Wajid M. Shaikh , Rupali S. Jain , B. Surendranath Reddy , Bhagyashri S. Patil , Sahar M. A. Maqbol

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 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 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

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

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 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

In this paper, we study a class of linear codes defined by characteristic functions of certain subsets of a finite field. We derive a sufficient and necessary condition for such a code to be a minimal linear code by a character-theoretical…

Combinatorics · Mathematics 2021-02-23 Ran Tao , Tao Feng , Weicong Li

In this paper, for an odd prime $p$, several classes of two-weight linear codes over the finite field $\mathbb{F}_p$ are constructed from the defining sets, and then their complete weight distributions are determined by employing character…

Information Theory · Computer Science 2021-11-22 Canze Zhu , Qunying Liao