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Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…

Information Theory · Computer Science 2014-08-19 Yixuan Xie , Jinhong Yuan , Yuichiro Fujiwara

Entanglement-assisted quantum error correcting codes (EAQECCs) are a simple and fundamental class of codes. They allow for the construction of quantum codes from classical codes by relaxing the duality condition and using pre-shared…

Information Theory · Computer Science 2016-06-02 Kenza Guenda , Somphong Jitman , T. Aaron Gulliver

In this paper, we construct new families of convolutional codes. Such codes are obtained by means of algebraic geometry codes. Additionally, more families of convolutional codes are constructed by means of puncturing, extending, expanding…

Information Theory · Computer Science 2021-07-27 Francisco Revson F. Pereira , Giuliano G. La Guardia , Francisco M. de Assis

Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…

Information Theory · Computer Science 2020-04-14 Ted Hurley , Donny Hurley , Barry Hurley

A set of quantum error correcting codes based on classical Reed-Muller codes is described. The codes have parameters [[n,k,d]] = [[2^r, 2^r - C(r,t) - 2 sum_{i=0}^{t-1} C(r,i), 2^t + 2^{t-1} ]].

Quantum Physics · Physics 2008-02-03 Andrew Steane

We explicitly construct an infinite family of asymptotically good concatenated quantum stabilizer codes where the outer code uses CSS-type quantum Reed-Solomon code and the inner code uses a set of special quantum codes. In the field of…

Quantum Physics · Physics 2009-01-06 Zhuo Li , Li-Juan Xing , Xin-Mei Wang

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

The theory of quantum error correction was established more than a decade ago as the primary tool for fighting decoherence in quantum information processing. Although great progress has already been made in this field, limited methods are…

Quantum Physics · Physics 2009-09-29 Zhuo Wang , Kai Sun , Hen Fan , Vlatko Vedral

Error-correcting codes for quantum computing are crucial to address the fundamental problem of communication in the presence of noise and imperfections. Audoux used Khovanov homology to define families of quantum error-correcting codes with…

Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed…

Quantum Physics · Physics 2015-03-10 Zunaira Babar , Panagiotis Botsinis , Dimitrios Alanis , Soon Xin Ng , Lajos Hanzo

We characterize the affine-invariant maximal extended cyclic codes. Then by the CSS construction, we derive from these codes a family of pure quantum codes. Also for ordnq even, a new family of degenerate quantum stabilizer codes is derived…

Information Theory · Computer Science 2007-11-14 Kenza Guenda

We present new constructions of quasi-cyclic (QC) and generalized quasi-cyclic (GQC) codes from algebraic curves. Unlike previous approaches based on elliptic curves, our method applies to curves that are Kummer extensions of the rational…

Information Theory · Computer Science 2026-02-06 Matteo Bonini , Arianna Dionigi , Francesco Ghiandoni

We present a new propagation rule for CSS codes. Starting with a CSS code $[\![n,k,d]\!]_q$, we construct a CSS code with parameters $[\![n-2,k,d-1]\!]_q$. In general, one would only obtain a code with parameters $[\![n-2,k,d-2]\!]_q$. The…

Quantum Physics · Physics 2023-10-06 Markus Grassl

Entanglement-assisted quantum error correcting codes (EAQECCs) constructed from Reed-Solomon codes and BCH codes are considered in this work. It is provided a complete and explicit formula for the parameters of EAQECCs coming from any…

Information Theory · Computer Science 2022-08-25 Carlos Galindo , Fernando Hernando , Diego Ruano

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

In this paper, we construct quantum synchronizable codes (QSCs) based on the sum and intersection of cyclic codes. Further, infinite families of QSCs are obtained from BCH and duadic codes. Moreover, we show that the work of…

Information Theory · Computer Science 2016-06-03 K. Guenda , G. G. La Guardia , T. A. Gulliver

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

One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…

Information Theory · Computer Science 2015-08-06 Tao Zhang , Gennian Ge

We discuss a method to construct quantum codes correcting amplitude damping errors via code concatenation. The inner codes are chosen as asymmetric Calderbank-Shor-Steane (CSS) codes. By concatenating with outer codes correcting symmetric…

Quantum Physics · Physics 2016-10-31 Tyler Jackson , Markus Grassl , Bei Zeng

Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…

Quantum Physics · Physics 2023-10-30 Diogo Cruz , Francisco A. Monteiro , Bruno C. Coutinho