Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1403.6192 · IEEE Information Theory Workshop (ITW)

Quantum synchronizable codes from quadratic residue codes and their supercodes

Yixuan Xie, Jinhong Yuan, Yuichiro Fujiwara

Published Nov 1, 2014• 23 citations
arXivHTMLPDF

Abstract

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 that satisfy special properties, only a few classes of cyclic codes have been proved to give promising quantum synchronizable codes. In this paper, using quadratic residue codes and their supercodes, we give a simple construction for quantum synchronizable codes whose synchronization capabilities attain the upper bound. The method is applicable to cyclic codes of prime length.

DOI
10.1109/itw.2014.6970815

Related papers

Quantum Synchronizable Codes on Sextic Cyclotomy

Tao Wang, Tongjiang Yan, Xueting Wang

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, the quantum synchronizable codes constructed are CSS quantum error-correcting codes whose synchronization capabilities reach the upper bound. And we use cyclic codes gained by sextic cyclotomic classes to construct two classes of quantum synchronizable codes. Moreover, the quantum synchronizable codes are posses good error-correcting capability towards bit error and phase error, since the cyclic codes we used are optimal or almost optimal.

arXiv:2105.03619•May 8, 2021•1 citation

A new family of quantum synchronizable codes from negacyclic codes

Tao Wang, Tongjiang Yan, Sun, Shiwen

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 synchronizable codes from negacyclic codes are proposed, where the length of these negacyclic codes are $p$ and $pq$. Through this method, the quantum synchronizable code possesses optimal or almost optimal error-correcting capability towards bits errors and phase errors, since the negacyclic codes we used are optimal or almost optimal. Moreover, this paper contributes to construct two classes quantum synchronizable codes, whose synchronization capabilities can reach the upper limit under certain conditions.

arXiv:2107.02648•Jul 6, 2021•0 citations

A New Family of Quantum Synchronizable Codes

Xia Li, Qin Yue

Quantum synchronizable codes (QSCs) are special quantum error-correcting codes that correct the effects of both quantum noise on qubits and misalignment in block synchronization. In this letter, we construct a family of QSCs from cyclic codes. The best attainable misalignment tolerance can also be achieved under certain constraints. And we give two classes of specific constructions of QSCs, which achieve the best attainable misalignment tolerance. Moreover, the second class of QSCs possess good error-correcting capability towards bit errors and phase errors.

IEEE Communications Letters•Sep 30, 2020•10 citations

Quantum Synchronizable Codes From Cyclotomic Classes of Order Two over $\mathbb{Z}_{2q}$

Tao Wang, Tongjiang Yan, Sidorenko, Vladimir +1 more

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. This paper contributes to constructing two classes of quantum synchronizable codes by the cyclotomic classes of order two over $\mathbb{Z}_{2q}$, whose synchronization capabilities can reach the upper bound under certain conditions. Moreover, the quantum synchronizable codes possess good error-correcting capability towards bit errors and phase errors.

arXiv:2106.02470•Jun 4, 2021•1 citation

Quantum Synchronizable Codes From Finite Geometries

Yuichiro Fujiwara, Peter Vandendriessche

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 code can be constructed through a combination of a classical linear code and its subcode if the two are both cyclic and dual-containing. However, finding such classical codes that lead to promising quantum synchronizable error-correcting codes is not a trivial task. In fact, although there are two families of classical codes that are proved to produce quantum synchronizable codes with good minimum distances and highest possible tolerance against misalignment, their code lengths have been restricted to primes and Mersenne numbers. In this paper, examining the incidence vectors of projective spaces over the finite fields of characteristic 2, we give quantum synchronizable codes from cyclic codes whose lengths are not primes or Mersenne numbers. These projective geometric codes achieve good performance in quantum error correction and possess the best possible ability to recover synchronization, thereby enriching the variety of good quantum synchronizable codes. We also extend the current knowledge of cyclic codes in classical coding theory by explicitly giving generator polynomials of the finite geometric codes and completely characterizing the minimum weight nonzero codewords. In addition to the codes based on projective spaces, we carry out a similar analysis on the well-known cyclic codes from Euclidean spaces that are known to be majority logic decodable and determine their exact minimum distances.

arXiv:1311.3416•IEEE Transactions on Information Theory•Sep 10, 2014•32 citations

Quantum Synchronizable Codes from Generalized Cyclotomy

Xueting Wang, Tongjiang Yan, Tao Wang +1 more

Quantum synchronizable codes can correct the ef-fects of quantum noise on qubits as well as misalignment in block synchronization. In this paper, dual-containing cyclic codes of length$2pq$and$p^{2}$are constructed by generalized cyclotomy, where some of the cyclic codes of length$p^{2}$are optimal or almost optimal. Based on these cyclic codes and their augmented codes, we obtain two new classes of quantum synchronizable codes whose synchronization capabilities are the best.

International Workshop on Signal Design and its Applications in Communications•Aug 1, 2022•2 citations
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 that satisfy special properties, only a few classes of cyclic codes have been proved to give promising quantum synchronizable codes. In this paper, using quadratic residue codes and their supercodes, we give a simple construction for quantum synchronizable codes whose synchronization capabilities attain the upper bound. The method is applicable to cyclic codes of prime length.
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, the quantum synchronizable codes constructed are CSS quantum error-correcting codes whose synchronization capabilities reach the upper bound. And we use cyclic codes gained by sextic cyclotomic classes to construct two classes of quantum synchronizable codes. Moreover, the quantum synchronizable codes are posses good error-correcting capability towards bit error and phase error, since the cyclic codes we used are optimal or almost optimal.
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 synchronizable codes from negacyclic codes are proposed, where the length of these negacyclic codes are ppp and pqpqpq. Through this method, the quantum synchronizable code possesses optimal or almost optimal error-correcting capability towards bits errors and phase errors, since the negacyclic codes we used are optimal or almost optimal. Moreover, this paper contributes to construct two classes quantum synchronizable codes, whose synchronization capabilities can reach the upper limit under certain conditions.
Quantum synchronizable codes (QSCs) are special quantum error-correcting codes that correct the effects of both quantum noise on qubits and misalignment in block synchronization. In this letter, we construct a family of QSCs from cyclic codes. The best attainable misalignment tolerance can also be achieved under certain constraints. And we give two classes of specific constructions of QSCs, which achieve the best attainable misalignment tolerance. Moreover, the second class of QSCs possess good error-correcting capability towards bit errors and phase errors.
Quantum Synchronizable Codes From Cyclotomic Classes of Order Two over Z2q\mathbb{Z}_{2q}Z2q​
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. This paper contributes to constructing two classes of quantum synchronizable codes by the cyclotomic classes of order two over Z2q\mathbb{Z}_{2q}Z2q​, whose synchronization capabilities can reach the upper bound under certain conditions. Moreover, the quantum synchronizable codes possess good error-correcting capability towards bit errors and phase errors.
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 code can be constructed through a combination of a classical linear code and its subcode if the two are both cyclic and dual-containing. However, finding such classical codes that lead to promising quantum synchronizable error-correcting codes is not a trivial task. In fact, although there are two families of classical codes that are proved to produce quantum synchronizable codes with good minimum distances and highest possible tolerance against misalignment, their code lengths have been restricted to primes and Mersenne numbers. In this paper, examining the incidence vectors of projective spaces over the finite fields of characteristic 2, we give quantum synchronizable codes from cyclic codes whose lengths are not primes or Mersenne numbers. These projective geometric codes achieve good performance in quantum error correction and possess the best possible ability to recover synchronization, thereby enriching the variety of good quantum synchronizable codes. We also extend the current knowledge of cyclic codes in classical coding theory by explicitly giving generator polynomials of the finite geometric codes and completely characterizing the minimum weight nonzero codewords. In addition to the codes based on projective spaces, we carry out a similar analysis on the well-known cyclic codes from Euclidean spaces that are known to be majority logic decodable and determine their exact minimum distances.
Quantum synchronizable codes can correct the ef-fects of quantum noise on qubits as well as misalignment in block synchronization. In this paper, dual-containing cyclic codes of length2pq2pq2pqandp2p^{2}p2are constructed by generalized cyclotomy, where some of the cyclic codes of lengthp2p^{2}p2are optimal or almost optimal. Based on these cyclic codes and their augmented codes, we obtain two new classes of quantum synchronizable codes whose synchronization capabilities are the best.