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Recently, linear codes with a few weights were widely investigated due to their applications in secret sharing schemes and authentication schemes. In this letter, we present a class of $q$-ary linear codes derived from irreducible cyclic…

Information Theory · Computer Science 2016-04-18 Ziling Heng , Qin Yue

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

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

For a linear Hamming metric code of length n over a finite field, the number of distinct weights of its codewords is at most n. The codes achieving the equality in the above bound were called full weight spectrum codes. In this paper we…

Information Theory · Computer Science 2024-05-31 Chiara Castello , Olga Polverino , Ferdinando Zullo

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

Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…

Information Theory · Computer Science 2012-07-12 Cunsheng Ding

Relative generalized Hamming weights (RGHWs) of a linear code respect to a linear subcode determine the security of the linear ramp secret sharing scheme based on the code. They can be used to express the information leakage of the secret…

Information Theory · Computer Science 2015-05-28 Jun Zhang , Keqin Feng

Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three zeros. Recently, \cite{Y-X-D12}…

Number Theory · Mathematics 2014-05-27 Jing Yang , Lingli Xia , Maosheng 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

Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…

Information Theory · Computer Science 2016-11-18 Cunsheng Ding

Based on cyclic and consta-cyclic simplex codes, a new explicit construction of a family of two-weight codes is presented. These two-weight codes obtained are in the form of 2-generator quasi-cyclic, or quasi-twisted structure. Based on…

Information Theory · Computer Science 2009-01-09 Eric Z. Chen

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

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

Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in…

Information Theory · Computer Science 2024-05-31 Wei Lu , Qingyao Wang , Xiaoqiang Wang , Dabin Zheng

In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring $R=\mathbb{F}_p+u\mathbb{F}_p+\cdots +u^{k-1}\mathbb{F}_{p},$ with $u^k=0,$ are constructed, which generalises…

Information Theory · Computer Science 2017-03-21 Minjia Shi , Rongsheng Wu , Liqin Qian , Lin Sok , Patrick Solé

In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring $R=\mathbb{F}_p+u\mathbb{F}_p+\cdots +u^{k-1}\mathbb{F}_{p},$ with $u^k=0,$ are constructed, which generalises…

Information Theory · Computer Science 2017-01-10 Minjia Shi , Rongsheng Wu , Liqin Qian , Lin Sok , Patrick Sole

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

Let p>3 be an odd prime and m be a positive integer. Little progress on the study of optimal p-ary cyclic codes with parameters [p^m-1,p^m-2m-2,4] has been made.In this paper, by weakening the necessary and sufficient conditions on cyclic…

Information Theory · Computer Science 2025-12-01 Jinmei Fan , Jingyao Feng , Yuhan Men , Yanhai Zhang

In this paper we extend the works \cite{gegeng2,XLZD} further in two directions and compute the weight distribution of these cyclic codes under more relaxed conditions. It is interesting to note that many cyclic codes in the family are…

Information Theory · Computer Science 2015-02-17 Maosheng Xiong , Nian Li

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