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

IEEE Access

Quantum AMDS Negacyclic Codes of Length 2 p s Over F p m

Hai Quang Dinh, Bac Trong Nguyen, Nui V Nguyen, Hiep L. Thi, Woraphon Yamaka

Published Aug 4, 2025• 0 citations
Publisher

Abstract

In this article, we investigate all almost maximum distance separable (briefly, AMDS) negacyclic codes of length 2psover the finite field Fpm, wherepis an odd prime. A necessary and sufficient condition for a code to be an AMDS and NMDS negacyclic code of length 2psover Fpmis also provided. In addition, we construct quantum AMDS (qAMDS) codes using both the Calderbank-Shor-Steane (CSS) and Hermitian constructions. These newly constructed codes have different parameters compared to previous constructions. Moreover, our qAMDS codes are better than all known quantum error correction (QEC) codes.

DOI
10.1109/access.2025.3595428

Related papers

Quantum MDS and Synchronizable Codes From Cyclic and Negacyclic Codes of Length 2ps Over F pm

Hai Quang Dinh, Bac Trong Nguyen, Woraphon Yamaka

Let p be an odd prime, and Fp(m)is the finite field of pmelements. In this paper, all maximum distance separable (briefly, MDS) cyclic and negacyclic codes of length 2psover Fp(m)are established. As an application, all quantum MDS (briefly, qMDS) codes are constructed from cyclic and negacyclic codes of length 2psover finite fields using the Calderbank Shor-Steane (briefly, CSS) and Hermitian constructions. These codes are new in the sense that their parameters are different from all the previous constructions. Furthermore, quantum synchronizable codes (briefly, QSCs) are obtained from cyclic codes of length 2psover Fp(m). To enrich the variety of available QSCs, many new QSCs are constructed to illustrate our results. Among them, there are QSCs codes with shorter lengths and much larger minimum distances than known primitive narrow-sense Bose-Chaudhuri-Hocquenghem (briefly, BCH) codes.

IEEE Access•Jan 1, 2020•16 citations

AMDS and quantum AMDS Constacyclic codes of length $4p^ς$ over $\mathbb{F}_{{p}^{m}}$

Manasa J, Divya Acharya, Prasanna Poojary

This paper provides a comprehensive analysis of almost maximum distance separable (AMDS) constacyclic codes of length $4p^ς$ over the finite field $\mathbb{F}_{p^m}$, where $p$ is an odd prime number. Furthermore, it introduces the construction of quantum AMDS (qAMDS) codes, drawing on the principles of the Calderbank-Shor-Steane (CSS) framework, which enhances their applicability in quantum error correction. This work aims to deepen the understanding of these codes and their potential uses in both classical and quantum computing environments.

arXiv:2605.23447•May 22, 2026•0 citations

New QEC codes and EAQEC codes from repeated-root cyclic codes of length $2^rp^s$

Lanqiang Li, Ziwen Cao, Tingting Wu +1 more

Let $p$ be an odd prime and $r,s,m$ be positive integers. In this study, we initiate our exploration by delving into the intricate structure of all repeated-root cyclic codes and their duals with a length of $2^rp^s$ over the finite field $\mathbb{F}_{p^m}$. Through the utilization of CSS and Steane's constructions, a series of new quantum error-correcting (QEC) codes are constructed with parameters distinct from all previous constructions. Furthermore, we provide all maximum distance separable (MDS) cyclic codes of length $2^rp^s$, which are further utilized in the construction of QEC MDS codes. Finally, we introduce a significant number of novel entanglement-assisted quantum error-correcting (EAQEC) codes derived from these repeated-root cyclic codes. Notably, these newly constructed codes exhibit parameters distinct from those of previously known constructions.

arXiv:2406.13943•Jun 20, 2024•0 citations

New Quantum MDS Codes From Negacyclic Codes

Xiaoshan Kai, Shixin Zhu

Letqbe an odd prime power. Based on classical negacyclic codes, we construct two classes of quantum maximum-distance-separable (MDS) codes with parameters [[q2+1,q2-2d+3,d]]qwhereq≡ 1 (mod 4) and 2 ≤d≤q+1 is even, and [[(q2+1)/2,(q2+1)/2-2d+2,d]]qwhere 3 ≤d≤qis odd. Some of these quantum MDS codes are new in the sense that their parameters are different from all the previously known ones.

IEEE Transactions on Information Theory•Sep 24, 2012•183 citations

Construction of quantum negacyclic BCH codes

Xiaoshan Kai, Li Ping, Shixin Zhu

Let [Formula: see text] be an odd prime power and [Formula: see text] be a positive integer. Maximum designed distance such that negacyclic BCH codes over [Formula: see text] of length [Formula: see text] are Hermitian dual-containing codes is given. The dimension of such Hermitian dual-containing negacyclic codes is completely determined by analyzing cyclotomic cosets. Quantum negacyclic BCH codes of length [Formula: see text] are obtained by using Hermitian construction. The constructed quantum negacyclic BCH codes produce new quantum codes with parameters better than those obtained from quantum BCH codes.

International Journal of Quantum Information•Oct 1, 2018•15 citations

A Class of Negacyclic Codes and Their Application to Quantum Codes

Junli Wang, Ruihu Li, Yang Liu +1 more

In this paper, the properties of q2-ary cyclotomic cosets modulo 2n are investigated in detail, where n=[(q2m-1)/(m(q-1))],q ≡ ±1mod m or q2≡ -1mod m when m is even and q is an odd power prime when m is power of 2. Then, non-narrow-sense negacyclic Bose-Chaudhuri-Hocquenghem (BCH) codes of length n that contain their Hermitian duals are determined. By the Hermitian construction, series of quantum codes are obtained from such negacyclic BCH codes. Compared with quantum codes in the [6], [10], [12], our constructed ones have better parameters.

International Congress on Image and Signal Processing (CISP)•Oct 1, 2019•0 citations
In this article, we investigate all almost maximum distance separable (briefly, AMDS) negacyclic codes of length 2psover the finite field Fpm, wherepis an odd prime. A necessary and sufficient condition for a code to be an AMDS and NMDS negacyclic code of length 2psover Fpmis also provided. In addition, we construct quantum AMDS (qAMDS) codes using both the Calderbank-Shor-Steane (CSS) and Hermitian constructions. These newly constructed codes have different parameters compared to previous constructions. Moreover, our qAMDS codes are better than all known quantum error correction (QEC) codes.
Let p be an odd prime, and Fp(m)is the finite field of pmelements. In this paper, all maximum distance separable (briefly, MDS) cyclic and negacyclic codes of length 2psover Fp(m)are established. As an application, all quantum MDS (briefly, qMDS) codes are constructed from cyclic and negacyclic codes of length 2psover finite fields using the Calderbank Shor-Steane (briefly, CSS) and Hermitian constructions. These codes are new in the sense that their parameters are different from all the previous constructions. Furthermore, quantum synchronizable codes (briefly, QSCs) are obtained from cyclic codes of length 2psover Fp(m). To enrich the variety of available QSCs, many new QSCs are constructed to illustrate our results. Among them, there are QSCs codes with shorter lengths and much larger minimum distances than known primitive narrow-sense Bose-Chaudhuri-Hocquenghem (briefly, BCH) codes.
AMDS and quantum AMDS Constacyclic codes of length 4pς4p^ς4pς over Fpm\mathbb{F}_{{p}^{m}}Fpm​
This paper provides a comprehensive analysis of almost maximum distance separable (AMDS) constacyclic codes of length 4pς4p^ς4pς over the finite field Fpm\mathbb{F}_{p^m}Fpm​, where ppp is an odd prime number. Furthermore, it introduces the construction of quantum AMDS (qAMDS) codes, drawing on the principles of the Calderbank-Shor-Steane (CSS) framework, which enhances their applicability in quantum error correction. This work aims to deepen the understanding of these codes and their potential uses in both classical and quantum computing environments.
New QEC codes and EAQEC codes from repeated-root cyclic codes of length 2rps2^rp^s2rps
Let ppp be an odd prime and r,s,mr,s,mr,s,m be positive integers. In this study, we initiate our exploration by delving into the intricate structure of all repeated-root cyclic codes and their duals with a length of 2rps2^rp^s2rps over the finite field Fpm\mathbb{F}_{p^m}Fpm​. Through the utilization of CSS and Steane's constructions, a series of new quantum error-correcting (QEC) codes are constructed with parameters distinct from all previous constructions. Furthermore, we provide all maximum distance separable (MDS) cyclic codes of length 2rps2^rp^s2rps, which are further utilized in the construction of QEC MDS codes. Finally, we introduce a significant number of novel entanglement-assisted quantum error-correcting (EAQEC) codes derived from these repeated-root cyclic codes. Notably, these newly constructed codes exhibit parameters distinct from those of previously known constructions.
Let [Formula: see text] be an odd prime power and [Formula: see text] be a positive integer. Maximum designed distance such that negacyclic BCH codes over [Formula: see text] of length [Formula: see text] are Hermitian dual-containing codes is given. The dimension of such Hermitian dual-containing negacyclic codes is completely determined by analyzing cyclotomic cosets. Quantum negacyclic BCH codes of length [Formula: see text] are obtained by using Hermitian construction. The constructed quantum negacyclic BCH codes produce new quantum codes with parameters better than those obtained from quantum BCH codes.
In this paper, the properties of q2-ary cyclotomic cosets modulo 2n are investigated in detail, where n=[(q2m-1)/(m(q-1))],q ≡ ±1mod m or q2≡ -1mod m when m is even and q is an odd power prime when m is power of 2. Then, non-narrow-sense negacyclic Bose-Chaudhuri-Hocquenghem (BCH) codes of length n that contain their Hermitian duals are determined. By the Hermitian construction, series of quantum codes are obtained from such negacyclic BCH codes. Compared with quantum codes in the [6], [10], [12], our constructed ones have better parameters.