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Related papers: Codes with few weights arising from linear sets

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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

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

Recently, linear codes with few weights have been constructed and extensively studied. In this paper, for an odd prime p, we determined the complete weight enumerator of two classes of p-ary linear codes constructed from defining set.…

Information Theory · Computer Science 2015-12-24 Qiuyan Wang , Fei Li , Kelan Ding , Dongdai Lin

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

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 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

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

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 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

Linear codes can be employed to construct authentication codes, which is an interesting area of cryptography. The parameters of the authentication codes depend on the complete weight enumerator of the underlying linear codes. In order to…

Information Theory · Computer Science 2015-05-27 Can Xiang , Hao Liu

Minimal linear codes have significant applications in secret sharing schemes and secure two-party computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many…

Information Theory · Computer Science 2018-08-14 Sihem Mesnager , Ahmet Sınak

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

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

Two-weight linear codes are linear codes in which any nonzero codeword can have only two possible distinct weights. Those in the Hamming metric have proven to be very interesting for their connections with authentication codes, association…

Information Theory · Computer Science 2024-05-07 Ferdinando Zullo , Olga Polverino , Paolo Santonastaso , John Sheekey

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 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

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

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

Linear codes with a few weights are very important in coding theory and have attracted a lot of attention. In this paper, we present a construction of $q$-ary linear codes from trace and norm functions over finite fields. The weight…

Information Theory · Computer Science 2017-07-25 Ziling Heng , Qin Yue

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