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Related papers: A Class of Linear Codes with a Few Weights

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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

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

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

Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of two-weight and three-weight linear codes are presented and their…

Information Theory · Computer Science 2019-05-08 Gaopeng Jian

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 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

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

Linear codes are the most important family of codes in cryptography and coding theory. Some codes have only a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs.…

Information Theory · Computer Science 2024-05-20 Shudi Yang , Tonghui Zhang , Zheng-An Yao

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 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 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

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

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, 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 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

Cyclic codes have been widely used in digital communication systems and consume electronics as they have efficient encoding and decoding algorithms. The weight distribution of cyclic codes has been an important topic of study for many…

Information Theory · Computer Science 2013-01-15 Jing Yang , Maosheng Xiong , Cunsheng Ding

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 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

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

Let $\mathbb{F}_{p^m}$ be the finite field of order $p^m$, where $p$ is an odd prime and $m$ is a positive integer. In this paper, we investigate a class of subfield codes of linear codes and obtain the weight distribution of…

Information Theory · Computer Science 2019-10-15 Xiaoqiang Wang , Dabin Zheng , Yan Zhang