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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

Recently, there has been intensive research on the weight distributions of cyclic codes. In this paper, we compute the weight distributions of three classes of cyclic codes with Niho exponents. More specifically, we obtain two classes of…

Information Theory · Computer Science 2014-01-10 Shuxing Li , Tao Feng , Gennian Ge

In this paper, several classes of three-weight ternary linear codes from non-weakly regular dual-bent functions are constructed based on a generic construction method. Instead of the whole space, we use the subspaces $B_+(f)$ or $B_-(f)$…

Information Theory · Computer Science 2022-01-19 Rumi Melih Pelen

Combinatorial designs are closely related to linear codes. In recent year, there are a lot of $t$-designs constructed from certain linear codes. In this paper, we aim to construct $2$-designs from binary three-weight codes. For any binary…

Information Theory · Computer Science 2023-12-22 Canze Zhu , Qunying Liao , Haibo Liu

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

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

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

In this paper, we propose a class of linear codes and obtain their weight distribution. Some of these codes are almost optimal. Moreover, several classes of constant composition codes(CCCs) are constructed as subcodes of linear codes.

Information Theory · Computer Science 2017-06-28 Long Yu , Xiusheng Liu

Coding theory and $t$-designs have close connections and interesting interplay. In this paper, we first introduce a class of ternary linear codes and study their parameters. We then focus on their three-weight subcodes with a special weight…

Information Theory · Computer Science 2019-02-07 Chunming Tang , Cunsheng Ding , Maosheng Xiong

Minimal codes are a class of linear codes which gained interest in the last years, thanks to their connections to secret sharing schemes. In this paper we provide the weight distribution and the parameters of families of minimal codes…

Combinatorics · Mathematics 2020-04-30 Daniele Bartoli , Matteo Bonini , Marco Timpanella

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

The weight hierarchy of a linear code has been an important research topic in coding theory since Wei's original work in 1991. Choosing $ D=\Big\{(x,y)\in \Big(\F_{p^{s_1}}\times\F_{p^{s_2}}\Big)\Big\backslash\{(0,0)\}: f(x)+g(y)=0\Big\}$…

Information Theory · Computer Science 2023-06-14 Xiumei Li , Fei Li

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

Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…

Information Theory · Computer Science 2025-11-25 Dongmei Huang , Qunying Liao , Sihem Mesnager , Gaohua Tang , Haode Yan

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

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

A projective linear code over $\mathbb{F}_q$ is called $\Delta$-divisible if all weights of its codewords are divisible by $\Delta$. Especially, $q^r$-divisible projective linear codes, where $r$ is some integer, arise in many applications…

Combinatorics · Mathematics 2019-12-24 Daniel Heinlein , Thomas Honold , Michael Kiermaier , Sascha Kurz , Alfred Wassermann

Recently, linear codes constructed from defining sets have been studied extensively. They may have nice parameters if the defining set is chosen properly. Let $ m >2$ be a positive integer. For an odd prime $ p $, let $ r=p^m $ and…

Information Theory · Computer Science 2017-04-10 Shudi Yang , Xiangli Kong , Chunming Tang

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

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