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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, a family of $p$-ary cyclic…

Information Theory · Computer Science 2013-02-06 Zhengchun Zhou , Cunsheng Ding , Jinquan Luo , Aixian Zhang

We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalize the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A.…

Information Theory · Computer Science 2017-02-10 Itzhak Tamo , Alexander Barg , Sreechakra Goparaju , Robert Calderbank

Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems…

Information Theory · Computer Science 2021-07-02 Nuh Aydin , R. Oliver VandenBerg

The cyclic code is a subclass of linear codes and has applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In 2013, Ding, et al. presented nine open…

Information Theory · Computer Science 2025-11-04 Peipei Zheng , Dong He , Qunying Liao

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

Cyclic codes are a subclass of linear codes and have wide applications in consumer electronics, data storage systems, and communication systems due to their efficient encoding and decoding algorithms. Cyclic codes with many zeros and their…

Information Theory · Computer Science 2013-01-25 Zhengchun Zhou , Aixian Zhang , Cunsheng Ding , Maosheng Xiong

In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and…

Information Theory · Computer Science 2017-04-03 Maosheng Xiong

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

We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and…

Information Theory · Computer Science 2015-02-06 Itzhak Tamo , Alexander Barg , Sreechakra Goparaju , Robert Calderbank

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

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

Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…

Information Theory · Computer Science 2024-12-03 Cunsheng Ding

Linear codes have been an interesting subject of study for many years, as linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a class of…

Information Theory · Computer Science 2016-01-27 Can Xiang , Chunming Tang , Keqin Feng

Cyclic codes are an interesting class of linear codes due to their efficient encoding and decoding algorithms as well as their theoretical importance. BCH codes form a subclass of cyclic codes and are very important in both theory and…

Information Theory · Computer Science 2016-08-09 Shuxing Li , Cunsheng Ding , Hao Liu

A lot of attention has been paid to the investigation of the algebraic properties of linear codes. In most cases, this investigation involves the determination of required code automorphisms, which are useful for decoders, such as the…

Combinatorics · Mathematics 2024-06-04 Ma Jicheng , Yan Guiying

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 $p\ge 5$ be an odd prime and $m$ be…

Information Theory · Computer Science 2022-08-31 Gaofei Wu , Huan Liu , Yuqing Zhang

We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since…

Rings and Algebras · Mathematics 2016-08-16 Delphine Boucher , Willi Geiselmann , Félix Ulmer

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

A characterization of a class of optimal three-weight cyclic codes of dimension 3 over any finite field was recently presented in [10]. Shortly after this, a generalization for the sufficient numerical conditions of such characterization…

Information Theory · Computer Science 2016-09-26 Gerardo Vega

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. Inspired by the recent work on binary cyclic codes published in…

Information Theory · Computer Science 2023-05-03 Tingfang Chen , Cunsheng Ding , Chengju Li , Zhonghua Sun