English
Related papers

Related papers: A Class of Three-Weight Cyclic Codes

200 papers

Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. Most previous results obtained so far were for cyclic codes with no more than three zeroes. Inspired by the works…

Information Theory · Computer Science 2018-06-21 Maosheng Xiong , Nian Li , Zhengchun Zhou , Cunsheng Ding

Cyclic codes have attracted a lot of research interest for decades as they have efficient encoding and decoding algorithms. In this paper, for an odd prime $p$, the weight distributions of two classes of $p$-ary cyclic codes are completely…

Information Theory · Computer Science 2017-07-07 Shudi Yang , Zheng-An Yao , Chang-An Zhao

Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we solve one more special case. The problem of finding the weight distribution is transformed into a…

Number Theory · Mathematics 2012-10-17 Maosheng Xiong

As a subclass of linear codes, cyclic codes have efficient encoding and decoding algorithms, so they are widely used in many areas such as consumer electronics, data storage systems and communication systems. In this paper, we give a…

Information Theory · Computer Science 2019-08-09 Yan Liu , Xiwang Cao

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Cyclic codes have been studied for many years, but their weight…

Information Theory · Computer Science 2013-06-25 Chengju Li , Qin Yue

Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made.…

Information Theory · Computer Science 2011-11-15 Cunsheng Ding

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let $m=2\ell+1$ for an integer $\ell\geq 1$…

Information Theory · Computer Science 2015-10-20 Cuiling Fan , Nian Li , Zhengchun Zhou

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

Cyclic codes, as a crucial subclass of linear codes, exhibit broad applications in communication systems, data storage systems, and consumer electronics, primarily attributed to their well-structured algebraic properties. Let $p$ denote an…

Information Theory · Computer Science 2025-09-15 Mengen Fang , Lanqiang Li , Fuyin Tian , Li Liu

Let $m\geq 3$ be an odd integer and $p$ be an odd prime. % with $p-1=2^rh$, where $h$ is an odd integer. In this paper, many classes of three-weight cyclic codes over $\mathbb{F}_{p}$ are presented via an examination of the condition for…

Information Theory · Computer Science 2013-08-28 Chunlei Li , Nian Li , Tor Helleseth , Cunsheng Ding

A class of optimal three-weight cyclic codes of dimension 3 over any finite field was presented by Vega [Finite Fields Appl., 42 (2016) 23-38]. Shortly thereafter, Heng and Yue [IEEE Trans. Inf. Theory, 62(8) (2016) 4501-4513] generalized…

Information Theory · Computer Science 2021-07-12 Gerardo Vega , Félix Hernández

Cyclic codes have efficient encoding and decoding algorithms. The decoding error probability and the undetected error probability are usually bounded by or given from the weight distributions of the codes. Most researches are about the…

Information Theory · Computer Science 2013-09-03 Xiaogang Liu , Yuan Luo

Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let $\alpha $ be a generator of…

Information Theory · Computer Science 2024-07-11 Gaofei Wu , Zhuohui You , Zhengbang Zha , Yuqing Zhang

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In this paper, we settle an open problem…

Combinatorics · Mathematics 2019-01-25 Dongchun Han , Haode Yan

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

An important family of codes for data storage systems, cryptography, consumer electronics, and network coding for error control in digital communications are the so-called cyclic codes. This kind of linear codes are also important due to…

Information Theory · Computer Science 2025-06-16 Gerardo Vega , Félix Hernández

Cyclic codes have efficient encoding and decoding algorithms over finite fields, so that they have practical applications in communication systems, consumer electronics and data storage systems. The objective of this paper is to give eight…

Information Theory · Computer Science 2022-05-02 Lanqiang Li , Li Liu , Shixin Zhu

In this paper, a family of five-weight reducible cyclic codes is presented. Furthermore, the weight distribution of these cyclic codes is determined, which follows from the determination of value distributions of certain exponential sums.

Information Theory · Computer Science 2015-02-13 Yan Liu , Haode Yan

In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these irreducible constacyclic codes and the parameters of their duals are settled. Several…

Information Theory · Computer Science 2022-07-06 Zhonghua Sun , Xiaoqiang Wang , Cunsheng Ding

Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we provide a slightly different approach toward the general problem and use it to solve one more special…

Number Theory · Mathematics 2011-11-15 Maosheng Xiong