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Quantum low-density parity-check (QLDPC) codes provide a practical balance between error-correction capability and implementation complexity in quantum error correction (QEC). In this paper, we propose an algebraic construction based on…

Information Theory · Computer Science 2026-01-14 Alessio Baldelli , Massimo Battaglioni , Jonathan Mandelbaum , Sisi Miao , Laurent Schmalen

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

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

Binary cyclic codes have been a hot topic for many years, and significant progress has been made in the study of this types of codes. As is well known, it is hard to construct infinite families of binary cyclic codes [n, n+1/2] with good…

Information Theory · Computer Science 2024-04-30 Tingting Wu , Lanqiang Li , Xiuyu Zhang , Shixin Zhu

Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…

PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…

Quantum Physics · Physics 2018-02-06 Nikolas P. Breuckmann

In this paper, we introduce a construction of quantum convolutional codes (QCCs) based on difference triangle sets (DTSs). To construct QCCs, one must determine polynomial stabilizers $X(D)$ and $Z(D)$ that commute (symplectic…

Information Theory · Computer Science 2026-02-17 Vahid Nourozi , David Mitchell

In this paper, we mainly use classical Hermitian self-orthogonal generalized Reed-Solomon codes to construct two new classes of quantum MDS codes. Most of our quantum MDS codes have minimum distance larger than q/2+1. Compared with…

Information Theory · Computer Science 2020-03-24 Weiwei Wang , Jiantao Li

Duadic group algebra codes are a generalization of quadratic residue codes. This paper settles an open problem raised by Zhu concerning the existence of duadic group algebra codes. These codes can be used to construct degenerate quantum…

Information Theory · Computer Science 2007-07-13 Salah A. Aly , Andreas Klappenecker , Pradeep Kiran Sarvepalli

We study finite-length qudit quantum low-density parity-check (LDPC) codes from translation-invariant CSS constructions on two-dimensional tori with twisted boundary conditions. Recent qubit work [PRX Quantum 6, 020357 (2025)] showed that,…

Quantum Physics · Physics 2026-02-05 Mourad Halla

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

Quantum computers will need effective error-correcting codes. Current quantum processors require precise control of each particle, so having fewer particles to control might be beneficial. Although traditionally quantum computers are…

Quantum Physics · Physics 2021-10-25 Arun J. Moorthy , Lane G. Gunderman

It has been a great challenge to construct new quantum MDS codes. In particular, it is very hard to construct quantum MDS codes with relatively large minimum distance. So far, except for some sparse lengths, all known $q$-ary quantum MDS…

Information Theory · Computer Science 2020-07-14 Lingfei Jin , Chaoping Xing

Building scalable quantum computers requires quantum error-correcting codes that enable reliable operations in the presence of noise. Motivated by such need, this paper introduces two constructions of high-rate, quantum dual-containing (DC)…

Information Theory · Computer Science 2026-05-13 Alessio Baldelli , Marco Baldi , Massimo Battaglioni , Franco Chiaraluce , Paolo Santini

In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to self-dual codes over finite chain rings.…

Information Theory · Computer Science 2017-04-24 Xiusheng Liu , Hualu Liu

One hurdle to performing reliable quantum computations is overcoming noise. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum computers.…

Quantum Physics · Physics 2022-04-27 Lane G. Gunderman

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

Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in protecting quantum information from decoherence and quantum noise. Recently, constructing entanglement-assisted quantum maximum distance separable…

Information Theory · Computer Science 2020-09-17 Wan Jiang , Shixin Zhu , Xiaojing 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

Constructing quantum LDPC codes with a minimum distance that grows faster than a square root of the length has been a major challenge of the field. With this challenge in mind, we investigate constructions that come from high-dimensional…

Quantum Physics · Physics 2020-04-20 Shai Evra , Tali Kaufman , Gilles Zémor