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Quasi-twisted (QT) codes are a generalization of quasi-cyclic (QC) codes. Based on consta-cyclic simplex codes, a new explicit construction of a family of 2-generator quasi-twisted (QT) two-weight codes is presented. It is also shown that…

Information Theory · Computer Science 2008-06-02 Eric Z. Chen

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

This paper consists of three parts. The first part presents a large class of new binary quasi-cyclic (QC)-LDPC codes with girth of at least 6 whose parity-check matrices are constructed based on cyclic subgroups of finite fields.…

Information Theory · Computer Science 2015-03-14 Li Zhang , Shu Lin , Khaled Abdel-Ghaffar , Zhi Ding , Bo Zhou

This paper aims to construct optimal quaternary additive codes with non-integer dimensions. Firstly, we propose combinatorial constructions of quaternary additive constant-weight codes, alongside additive generalized anticode construction.…

Information Theory · Computer Science 2024-11-12 Chaofeng Guan , Jingjie Lv , Gaojun Luo , Zhi Ma

We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear…

Quantum Physics · Physics 2009-07-30 Peter W. Shor , Graeme Smith , John A. Smolin , Bei Zeng

A superimposed code is a collection of binary vectors (codewords) with the property that no vector is contained in the Boolean sum of any $k$ others, enabling unique identification of codewords within any group of $k$. Superimposed codes…

Data Structures and Algorithms · Computer Science 2025-08-05 Gianluca De Marco , Dariusz R. Kowalski

In this note, we present a construction of new nonbinary quantum codes with good parameters. These codes are obtained by applying the Calderbank-Shor-Steane (CSS) construction. In order to do this, we show the existence of (classical)…

Quantum Physics · Physics 2017-05-24 Giuliano G. La Guardia

A novel code construction based on spatially coupled low-density parity-check (SC-LDPC) codes is presented. The proposed code ensembles are described by protographs, comprised of several protograph-based chains characterizing individual…

Information Theory · Computer Science 2016-11-18 Dmitri Truhachev , David G. M. Mitchell , Michael Lentmaier , Daniel J. Costello

Entanglement-assisted quantum error-correcting codes (EAQECCs) to desired rate, error-correcting capability and maximum shared entanglement are constructed. Thus for a required rate $R$, required error-correcting capability to correct $t$…

Information Theory · Computer Science 2019-03-05 Ted Hurley , Donny Hurley , Barry Hurley

The theory of entanglement-assisted quantum error-correcting codes (EAQECCs) is a generalization of the standard stabilizer quantum error-correcting codes, which can be possibly constructed from any classical codes by relaxing the duality…

Information Theory · Computer Science 2023-05-16 Xiaojing Chen , Xingbo Lu , Shixin Zhu , Wan Jiang , Xindi Wang

In this paper, ensembles of quasi-cyclic moderate-density parity-check (MDPC) codes based on protographs are introduced and analyzed in the context of a McEliece-like cryptosystem. The proposed ensembles significantly improve the error…

Information Theory · Computer Science 2018-01-24 Gianluigi Liva , Hannes Bartz

We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes,…

Quantum Physics · Physics 2007-09-13 Sixia Yu , Qing Chen , C. H. Oh

We present several novel encodings for cardinality constraints, which use fewer clauses than previous encodings and, more importantly, introduce new generally applicable techniques for constructing compact encodings. First, we present a CNF…

Computational Complexity · Computer Science 2026-04-20 Andrew Krapivin , Benjamin Przybocki , Bernardo Subercaseaux

Let $r,s,t$ be three positive integers and $\mathcal{C}$ be a binary linear code of lenght $r+s+t$. We say that $\mathcal{C}$ is a triple cyclic code of lenght $(r,s,t)$ over $\mathbb{Z}_2$ if the set of coordinates can be partitioned into…

Information Theory · Computer Science 2015-09-18 Hojjat Mostafanasab

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

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

Communication in the presence of bounded timing asynchronism which is known to the receiver but cannot be easily compensated is studied. Examples of such situations include point-to-point communication over inter-symbol interference (ISI)…

Information Theory · Computer Science 2014-11-18 Ping-Chung Wang , Yu-Chih Huang , Krishna R. Narayanan

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

Spatially-coupled (SC) LDPC codes have recently emerged as an excellent choice for error correction in modern data storage and communication systems due to their outstanding performance. It has long been known that irregular graph codes…

Information Theory · Computer Science 2019-06-17 Homa Esfahanizadeh , Ruiyi Wu , Lara Dolecek

Quantum synchronizable codes (QSCs) are special quantum error-correcting codes which can be used to correct the effects of quantum noise on qubits and misalignment in block synchronization. In this paper, a new class of quantum…

Quantum Physics · Physics 2021-10-27 Shiwen Sun , Tongjiang Yan , Yuhua Sun , Tao Wang , Xueting Wang