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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, almost perfect nonlinear…

Information Theory · Computer Science 2012-06-22 Cunsheng Ding

One of the main goals of coding theory is to construct codes with best possible parameters and properties. A special class of codes called quasi-twisted (QT) codes is well-known to produce codes with good parameters. Most of the work on QT…

Information Theory · Computer Science 2021-08-25 Dev Akre , Nuh Aydin , Matthew J. Harrington , Saurav R. Pandey

Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this…

Information Theory · Computer Science 2017-01-05 Nuh Aydin , Ajdin Halilovic

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 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

In addition to their applications in data storage, communications systems, and consumer electronics, LCD codes -- a class of linear codes -- have been employed in cryptography recently. LCD cyclic codes were referred to as reversible cyclic…

Information Theory · Computer Science 2017-01-03 Chengju Li , Cunsheng Ding , Shuxing Li

In this paper we investigate the class of constacyclic codes, which is a natural generalization of the class of cyclic and negacyclic codes. This class of codes is interesting in the sense that it contains codes with good or even optimal…

Information Theory · Computer Science 2016-02-12 Giuliano G. La Guardia

In this paper, a new method is given for counting cycles in the Tanner graph of a (Type-I) quasi-cyclic (QC) low-density parity-check (LDPC) code which the complexity mainly is dependent on the base matrix, independent from the CPM-size of…

Information Theory · Computer Science 2023-10-20 Mohammad Gholami , Zahra Gholami

Cyclic codes are an important subclass of linear codes with wide applications in communication systems and data storage systems. In 2013, Ding and Helleseth presented nine open problems on optimal ternary cyclic codes $\mathcal{C}_{(1,e)}$.…

Information Theory · Computer Science 2026-01-21 Jingjun Bao , Hanlin Zou

Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional…

Information Theory · Computer Science 2017-07-17 Bocong Chen , Hongwei Liu

It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…

Information Theory · Computer Science 2023-01-09 Chaofeng Guan , Ruihu Li , Liangdong Lu , Yu Yao

Based on good algebraic structures and practicabilities, generalized quasi-cyclic (GQC) codes play important role in coding theory. In this paper, we study some results on GQC codes over $\mathbb{Z}_4$ including the normalized generating…

Rings and Algebras · Mathematics 2022-03-24 Jian Gao , Xiangrui Meng , Fang-Wei Fu

We construct new families of completely regular codes by concatenation methods. By combining parity check matrices of cyclic Hamming codes, we obtain families of completely regular codes. In all cases, we compute the intersection array of…

Combinatorics · Mathematics 2017-03-20 J. Borges , J. Rifà , V. Zinoviev

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, monomials and trinomials over…

Information Theory · Computer Science 2013-10-08 Cunsheng Ding , Zhengchun Zhou

The problem of identifying whether the family of cyclic codes is asymptotically good or not is a long-standing open problem in the field of coding theory. It is known in the literature that some families of cyclic codes such as BCH codes…

Information Theory · Computer Science 2017-05-30 Arti Yardi , Ruud Pellikaan

Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder…

Information Theory · Computer Science 2017-02-02 Cem Güneri , Ferruh Özbudak , Buket Özkaya , Elif Saçıkara , Zahra Sepasdar , Patrick Solé

Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a…

Quantum Physics · Physics 2014-11-17 Yuichiro Fujiwara , Peter Vandendriessche

Based on cyclic simplex codes, a new construction of a family of 2-generator quasi-cyclic two-weight codes is given. New optimal binary quasi-cyclic [195, 8, 96], [210, 8, 104] and [240, 8, 120] codes, good QC ternary [195, 6, 126], [208,…

Information Theory · Computer Science 2007-07-13 Eric Zhi Chen

Quadratic residue codes have been one of the most important classes of algebraic codes. They have been generalized into duadic codes and quadratic double circulant codes. In this paper we introduce a new subclass of double circulant codes,…

Information Theory · Computer Science 2012-02-07 Sunghyu Han , Jon-Lark Kim

This paper considers the equivalence problem for quasi-cyclic codes over finite fields. The results obtained are used to construct isodual quasi-cyclic codes.

Information Theory · Computer Science 2016-07-27 Kenza Guenda , T. Aaron Gulliver