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

Modern Physics Letters B

NONBINARY QUANTUM CODES DERIVED FROM REPEATED-ROOT CYCLIC CODES

Jianfa Qian, LINA ZHANG

Published Mar 4, 2013• 7 citations
Publisher

Abstract

Many good quantum error-correcting codes were constructed from cyclic codes. However, it is a difficult problem to determine the true minimum distance of quantum cyclic codes for large length n. In this work, we construct nonbinary quantum cyclic codes and asymmetric quantum cyclic codes that are derived from repeated-root cyclic codes for an arbitrary length ps, and determine the true minimum distance of all those codes. Some proposed quantum cyclic codes are optimal. Additionally, some proposed asymmetric quantum cyclic codes have better parameters than the ones available in the literature.

DOI
10.1142/s021798491350053x

Related papers

Non-Binary Quantum Synchronizable Codes From Repeated-Root Cyclic Codes

Lan Luo, Zhi Ma

In this paper, we construct a new family of quantum synchronizable codes from repeated-root cyclic codes of lengths psand lpsover Fq, where s 1 andl ≥ 2 are integers, and p ≥ 3 is the odd characteristic. Within some loose limitations, these synchronizable codes can possess the best possible capability in synchronization recovery, and therefore, enriches the variety of good quantum synchronizable codes. Furthermore, by using known techniques in classical coding theory which convert the computation of the minimum distance of a repeated-root cyclic code to that of a shorter simple-root cyclic code, we prove that the repeated-root cyclic codes of lengths ps and l ps are in general better than narrow-sense BCH codes of close lengths in terms of minimum distances, and thereby enable the obtained synchronizable codes to correct more Pauli errors.

IEEE Transactions on Information Theory•Jan 19, 2018•35 citations

NONBINARY QUANTUM CODES DERIVED FROM GROUP CHARACTER CODES

Jianfa Qian, Lina Zhang

Most of quantum codes have been constructed by using classical linear codes over finite field. However, little is known about the construction of quantum codes via group character codes. In this work, we present the constructions of nonbinary quantum and asymmetric quantum codes based on group character codes, and give explicit parameters for infinite families of nonbinary quantum codes and asymmetric quantum codes. Furthermore, we present families of optimal quantum codes which derived from group character codes.

International Journal of Quantum Information•Jun 1, 2012•10 citations

On non-binary quantum repeated-root cyclic codes

Liqi Wang, Shixin Zhu

In this paper, based on the Steane's enlargement construction, three classes of non-binary quantum codes are constructed from classical repeated-root cyclic codes of length 2ps over 𝔽q with odd characteristic p. The exact minimum distances of these quantum codes are determined. This construction yields a quantum MDS code with parameters [[2p, 2p - 4, 3]]p and two good quantum codes with parameters [[2p, 2p - 7, 4]]p and [[2p, 2p - 10, 5]]p.

International Journal of Quantum Information•Apr 1, 2014•5 citations

ON TWO PROBLEMS OF ASYMMETRIC QUANTUM CODES

Ruihu Li, Genqi Xu, Luobin Guo

In this paper, we discuss two problems on asymmetric quantum error-correcting codes (AQECCs). The first one is on the construction of a [[12, 1, 5/3]]2asymmetric quantum code, we show an impure [[12, 1, 5/3 ]]2exists. The second one is on the construction of AQECCs from binary cyclic codes, we construct many families of new asymmetric quantum codes with dz> δmax+1 from binary primitive cyclic codes of length n = 2m-1, where δmax= 2⌈m/2⌉-1 is the maximal designed distance of dual containing narrow sense BCH code of length n = 2m-1. A number of known codes are special cases of the codes given here. Some of these AQECCs have parameters better than the ones available in the literature.

International Journal of Modern Physics B•Dec 6, 2013•11 citations

QUANTUM CODES CONSTRUCTED FROM BINARY CYCLIC CODES

Ruihu Li, Xueliang Li

In this paper, we use 2-cyclotomic cosets of modulo n and generator polynomials to describe binary cyclic codes of length N=2αn with n odd. We discuss the conditions under which two cyclic codes [Formula: see text] and [Formula: see text] can be used to construct quantum codes by CSS construction or Steane's construction. Using the results of Chen, Promhouse and Tavares, and Castagnoli et al., we study the quantum codes that can be constructed from binary cyclic codes of length N=2αn with n odd and n≤99, and α≤2. We find that except the quantum codes constructed by Steane, there are also some very interesting quantum codes constructed from repeated-root cyclic codes, and some of the quantum codes constructed by Steane can be improved.

International Journal of Quantum Information•Jun 1, 2004•27 citations

Construction of Asymmetric Quantum Product Codes Based Repeated-Root Cyclic Codes

Pan Yue Fu, Wei Liu

A kind of classical product codes based on repeated-root cyclic codes are considered in this paper, and the classical product codes are applied to construct the asymmetric quantum product codes. The novel asymmetric quantum product codes have great asymmetry for correcting Z errors and X errors, and the parameters of asymmetric quantum product codes can be precisely determined by the properties of the repeated-root cyclic codes and their dual codes. The examples show that these asymmetric quantum product codes based repeated-root cyclic codes are more efficient than some existent asymmetric quantum product codes.

Applied Mechanics and Materials•Sep 1, 2014•0 citations
Many good quantum error-correcting codes were constructed from cyclic codes. However, it is a difficult problem to determine the true minimum distance of quantum cyclic codes for large length n. In this work, we construct nonbinary quantum cyclic codes and asymmetric quantum cyclic codes that are derived from repeated-root cyclic codes for an arbitrary length ps, and determine the true minimum distance of all those codes. Some proposed quantum cyclic codes are optimal. Additionally, some proposed asymmetric quantum cyclic codes have better parameters than the ones available in the literature.
In this paper, we construct a new family of quantum synchronizable codes from repeated-root cyclic codes of lengths psand lpsover Fq, where s 1 andl ≥ 2 are integers, and p ≥ 3 is the odd characteristic. Within some loose limitations, these synchronizable codes can possess the best possible capability in synchronization recovery, and therefore, enriches the variety of good quantum synchronizable codes. Furthermore, by using known techniques in classical coding theory which convert the computation of the minimum distance of a repeated-root cyclic code to that of a shorter simple-root cyclic code, we prove that the repeated-root cyclic codes of lengths ps and l ps are in general better than narrow-sense BCH codes of close lengths in terms of minimum distances, and thereby enable the obtained synchronizable codes to correct more Pauli errors.
Most of quantum codes have been constructed by using classical linear codes over finite field. However, little is known about the construction of quantum codes via group character codes. In this work, we present the constructions of nonbinary quantum and asymmetric quantum codes based on group character codes, and give explicit parameters for infinite families of nonbinary quantum codes and asymmetric quantum codes. Furthermore, we present families of optimal quantum codes which derived from group character codes.
In this paper, we discuss two problems on asymmetric quantum error-correcting codes (AQECCs). The first one is on the construction of a [[12, 1, 5/3]]2asymmetric quantum code, we show an impure [[12, 1, 5/3 ]]2exists. The second one is on the construction of AQECCs from binary cyclic codes, we construct many families of new asymmetric quantum codes with dz> δmax+1 from binary primitive cyclic codes of length n = 2m-1, where δmax= 2⌈m/2⌉-1 is the maximal designed distance of dual containing narrow sense BCH code of length n = 2m-1. A number of known codes are special cases of the codes given here. Some of these AQECCs have parameters better than the ones available in the literature.
In this paper, we use 2-cyclotomic cosets of modulo n and generator polynomials to describe binary cyclic codes of length N=2αn with n odd. We discuss the conditions under which two cyclic codes [Formula: see text] and [Formula: see text] can be used to construct quantum codes by CSS construction or Steane's construction. Using the results of Chen, Promhouse and Tavares, and Castagnoli et al., we study the quantum codes that can be constructed from binary cyclic codes of length N=2αn with n odd and n≤99, and α≤2. We find that except the quantum codes constructed by Steane, there are also some very interesting quantum codes constructed from repeated-root cyclic codes, and some of the quantum codes constructed by Steane can be improved.
A kind of classical product codes based on repeated-root cyclic codes are considered in this paper, and the classical product codes are applied to construct the asymmetric quantum product codes. The novel asymmetric quantum product codes have great asymmetry for correcting Z errors and X errors, and the parameters of asymmetric quantum product codes can be precisely determined by the properties of the repeated-root cyclic codes and their dual codes. The examples show that these asymmetric quantum product codes based repeated-root cyclic codes are more efficient than some existent asymmetric quantum product codes.