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

International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC)

Dual Containing BCH Codes and New Asymmetric Quantum Codes

Yuena Ma, Xiaoyi Feng, Liangdong Lv, Jiakun Li

Published Sep 1, 2015• 2 citations
Publisher

Abstract

In this paper, we discuss the problem on the construction of asymmetric quantum codes [[n,k,dz /dx]]4from primitive narrow sense BCH codes. Take advantage of dual containing BCH codes of length n = 4m- 1 where m = 2l and mm =2l±1 , we construct two families of new asymmetric quantum codes with dz≥ δmax+1, where δmaxis the maximal designed distance of dual containing narrow sense BCH code. Our asymmetric quantum codes are new ones, and are not included in the known literature.

DOI
10.1109/imccc.2015.334

Related papers

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

Two families of BCH codes and construction of quantum codes

Yuena Ma, Genqi Xu

Let q ≥ 3 be odd prime power. Maximal designed distances of non-primitive Hermitian dual containing q2- ary BCH codes of length n = (q4-1)/2 and 2(q2-1) are determined. For each given n, a group of non-narrow-sense Hermitian dual containing BCH codes are constructed and their dimensions are computed. Using these non-narrow-sense BCH codes, many new quantum codes are constructed. Our maximal designed distances improve upon the known results in the literature and many of new quantum BCH codes are better than those constructed from narrow-sense BCH codes.

International Conference on Information Science, Electronics and Electrical Engineering•Apr 1, 2014•1 citation

New Quantum BCH codes of Length n = q 2l+1 − 1

Yang Liu, Guanmin Guo, Yunmin Huang +2 more

Let q ≥ 4 be a prime power. This paper aims to construct new quantum Bose-Chaudhuri-Hocquenghem (BCH) codes of length n = q 2 l +1 − 1. We first determine the maximum designed distance of Euclidean dual containing non-narrow-sense q -ary BCH codes of length n . Applying Steane construction to these codes, new non-narrow-sense primitive quantum BCH codes shall be obtained, whose parameters are determined and better than ones in the literature.

Journal of Physics Conference Series•Aug 1, 2018•0 citations

A class of imprimitive BCH codes and new quantum codes

Yang Liu, Yuena Ma, Ruihu Li +1 more

Let q be a prime power, l ≥ 2 be even, n=(q-1)(qil-1)/(qi-1). We give necessary and sufficient conditions on dual containing q-ary narrow-sense BCH codes of lengthn, and improve previous upper bound on necessary condition. We present a family of dual containing non-narrow-sense BCH codes of lengthnincluding the BCH code with maximal designed distance, calculate their dimensions and use them to construct new quantum codes, which are better than those constructed from narrow-sense BCH codes.

International Conference on Computer Science and Information Processing•Aug 1, 2012•0 citations

Asymmetric Quantum Codes of Large Z - Distance Constructed from a Class of Quaternary Imprimitive BCH Codes

Ruihu Li, Genqi Xu, Qiang Fu +1 more

In this paper, we focus on construction of asymmetric quantum error-correcting codes (AQECCs) from quaternary narrow-sense BCH codes of code length n = 4m-1/3(m≥3 is an integer) via Calderbank-Shor-Steane construction. By a careful analysis on properties of cyclotomic cosets in the defining sets of two ingredient BCH codes B(n, δ1)4and B(n,δ2)4that satisfies B⊥h(n,δ1)4⊆ B(n,δ2)4used for constructing AQECCs, we derive new families of AQECCs with dz> δmaxs+ 1, and thus we can eliminate the unreasonable restriction dz≤ δmaxdevised in previous literature and obtain new AQECCs with greater asymmetry compared with the known results. Here δmaxsis the maximal designed distance of Hermitian dual-containing narrow-sense BCH codes of length n = 4m-1/3.

International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC)•Sep 1, 2015•0 citations

NEW QUANTUM CODES CONSTRUCTED FROM A CLASS OF IMPRIMITIVE BCH CODES

Yang Liu, Yuena Ma, Youqian Feng +1 more

By a careful analysis on cyclotomic cosets, the maximal designed distance δnew of narrow-sense imprimitive Euclidean dual containing q-ary BCH code of length [Formula: see text] is determined, where q is a prime power and l is odd. Our maximal designed distance δnew of dual containing narrow-sense BCH codes of length n improves upon the lower bound δmax for maximal designed distances of dual containing narrow-sense BCH codes given by Aly et al. [IEEE Trans. Inf. Theory53 (2007) 1183]. A series of non-narrow-sense dual containing BCH codes of length n, including the ones whose designed distances can achieve or exceed δnew, are given, and their dimensions are computed. Then new quantum BCH codes are constructed from these non-narrow-sense imprimitive BCH codes via Steane construction, and these new quantum codes are better than previous results in the literature.

International Journal of Quantum Information•Feb 1, 2013•9 citations
In this paper, we discuss the problem on the construction of asymmetric quantum codes [[n,k,dz /dx]]4from primitive narrow sense BCH codes. Take advantage of dual containing BCH codes of length n = 4m- 1 where m = 2l and mm =2l±1 , we construct two families of new asymmetric quantum codes with dz≥ δmax+1, where δmaxis the maximal designed distance of dual containing narrow sense BCH code. Our asymmetric quantum codes are new ones, and are not included in the known literature.
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.
Let q ≥ 3 be odd prime power. Maximal designed distances of non-primitive Hermitian dual containing q2- ary BCH codes of length n = (q4-1)/2 and 2(q2-1) are determined. For each given n, a group of non-narrow-sense Hermitian dual containing BCH codes are constructed and their dimensions are computed. Using these non-narrow-sense BCH codes, many new quantum codes are constructed. Our maximal designed distances improve upon the known results in the literature and many of new quantum BCH codes are better than those constructed from narrow-sense BCH codes.
In this paper, we focus on construction of asymmetric quantum error-correcting codes (AQECCs) from quaternary narrow-sense BCH codes of code length n = 4m-1/3(m≥3 is an integer) via Calderbank-Shor-Steane construction. By a careful analysis on properties of cyclotomic cosets in the defining sets of two ingredient BCH codes B(n, δ1)4and B(n,δ2)4that satisfies B⊥h(n,δ1)4⊆ B(n,δ2)4used for constructing AQECCs, we derive new families of AQECCs with dz> δmaxs+ 1, and thus we can eliminate the unreasonable restriction dz≤ δmaxdevised in previous literature and obtain new AQECCs with greater asymmetry compared with the known results. Here δmaxsis the maximal designed distance of Hermitian dual-containing narrow-sense BCH codes of length n = 4m-1/3.
By a careful analysis on cyclotomic cosets, the maximal designed distance δnew of narrow-sense imprimitive Euclidean dual containing q-ary BCH code of length [Formula: see text] is determined, where q is a prime power and l is odd. Our maximal designed distance δnew of dual containing narrow-sense BCH codes of length n improves upon the lower bound δmax for maximal designed distances of dual containing narrow-sense BCH codes given by Aly et al. [IEEE Trans. Inf. Theory53 (2007) 1183]. A series of non-narrow-sense dual containing BCH codes of length n, including the ones whose designed distances can achieve or exceed δnew, are given, and their dimensions are computed. Then new quantum BCH codes are constructed from these non-narrow-sense imprimitive BCH codes via Steane construction, and these new quantum codes are better than previous results in the literature.