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Related papers: On Negacyclic MDS-Convolutional Codes

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Several new families of multi-memory classical convolutional Bose-Chaudhuri-Hocquenghem (BCH) codes as well as families of unit-memory quantum convolutional codes are constructed in this paper. Our unit-memory classical and quantum…

Quantum Physics · Physics 2016-11-17 Giuliano G. La Guardia

New infinite families of quantum symmetric and asymmetric codes are constructed. Several of these are MDS. The codes obtained are shown to have parameters which are better than previously known. A number of known codes are special cases of…

Information Theory · Computer Science 2012-08-14 Kenza Guenda , T. Aaron Gulliver

Constacyclic codes are important classes of linear codes that have been applied to the construction of quantum codes. Six new families of asymmetric quantum codes derived from constacyclic codes are constructed in this paper. Moreover, the…

Information Theory · Computer Science 2014-04-01 Liqi Wang , Shixin Zhu

Constacyclic codes contain cyclic codes as a subclass and have nice algebraic structures. Constacyclic codes have theoretical importance, as they are connected to a number of areas of mathematics and outperform cyclic codes in several…

Information Theory · Computer Science 2023-01-26 Zhonghua Sun , Cunsheng Ding

In this paper, we construct the first families of asymmetric quantum convolutional codes (AQCC)'s. These new AQCC's are constructed by means of the CSS-type construction applied to suitable families of classical convolutional codes, which…

Quantum Physics · Physics 2016-10-05 Giuliano G. La Guardia

Linear codes with complementary duals (LCD) have a great deal of significance amongst linear codes. Maximum distance separable (MDS) codes are also an important class of linear codes since they achieve the greatest error correcting and…

Information Theory · Computer Science 2019-09-17 Mehmet E. Koroglu , Mustafa Sarı

In this paper, we construct a new family of distance-optimal binary cyclic codes with the minimum distance $6$ and a new family of distance-optimal quaternary cyclic codes with the minimum distance $4$. We also construct several families of…

Information Theory · Computer Science 2024-02-15 Hao Chen , Yanan Wu

In this paper, two new families of MDS quantum convolutional codes are constructed. The first one can be regarded as a generalization of \cite[Theorem 6.5]{GGGlinear}, in the sense that we do not assume that $q\equiv1\pmod{4}$. More…

Information Theory · Computer Science 2015-06-22 Guanghui Zhang , Bocong Chen , Liangchen Li

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

Maximum-distance separable (MDS) convolutional codes form an optimal family of convolutional codes, the study of which is of great importance. There are very few general algebraic constructions of MDS convolutional codes. In this paper, we…

Information Theory · Computer Science 2015-11-24 Chin Hei Chan , Maosheng Xiong

We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them…

Quantum Physics · Physics 2009-11-13 Zhuo Li , Li-Juan Xing , Xin-Mei Wang

In this paper, we analyze $m$-dimensional ($m$D) convolutional codes with finite support, viewed as a natural generalization of one-dimensional (1D) convolutional codes to higher dimensions. An $m$D convolutional code with finite support…

Information Theory · Computer Science 2026-03-26 Z. Abreu , J. Lieb , R. Pinto , R. Simoes

We generalized to higher dimensions the notions of optical orthogonal codes. We establish uper bounds on the capacity of general $ n $-dimensional OOCs, and on specific types of ideal codes (codes with zero off-peak autocorrelation). The…

Combinatorics · Mathematics 2022-07-18 Tim Alderson

Recently, entanglement-assisted quantum error correcting codes (EAQECCs) have been constructed by cyclic codes and negacyclic codes. In this paper, by analyzing the cyclotomic cosets in the defining set of constacyclic codes, we constructed…

Information Theory · Computer Science 2018-03-02 Xiaojing Chen , Shixin Zhu , Xiaoshan Kai

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

We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary…

Quantum Physics · Physics 2023-11-27 Markus Grassl , Thomas Beth , Martin Roetteler

Maximum-distance separable (MDS) convolutional codes are characterized by the property that their free distance reaches the generalized Singleton bound. In this paper, new criteria to construct MDS convolutional codes are presented.…

Information Theory · Computer Science 2023-05-26 Zita Abreu , Julia Lieb , Raquel Pinto , Joachim Rosenthal

Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian…

Information Theory · Computer Science 2014-03-12 Bocong Chen , San Ling , Guanghui Zhang

Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, a new method for construct quantum…

Quantum Physics · Physics 2022-03-21 Tao Wang , Tongjiang Yan , Shiwen Sun

This paper is devoted to the study of the construction of new quantum MDS codes. Based on constacyclic codes over Fq2 , we derive four new families of quantum MDS codes, one of which is an explicit generalization of the construction given…

Information Theory · Computer Science 2017-05-08 Mustafa Sari , Emre Kolotoglu
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