A study of QECCs and EAQECCs construction from cyclic codes over the ring Fq+v1Fq+v2Fq+<middle dot><middle dot><middle dot>+vsFq

被引：0
|
作者：
Pandey, Om Prakash [1 ]
Pathak, Sachin [2 ]
Shukla, Awadhesh Kumar [1 ]
Mishra, Vipul [1 ]
Upadhyay, Ashish Kumar [1 ]
机构：
[1] Banaras Hindu Univ, Dept Math, Varanasi 221005, Uttar Pradesh, India
[2] NIIT Univ, Dept Math & Basic Sci, Neemrana 301705, India
来源：
QUANTUM INFORMATION PROCESSING | 2024年 / 23卷 / 02期
关键词：
Cyclic codes; Generator polynomials; Euclidean sums and hulls of cyclic codes; QECCs and EAQECCs; QUANTUM CODES; CONSTACYCLIC CODES; MDS CODES;
D O I：
10.1007/s11128-023-04240-6
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, we present a construction of quantum error-correcting codes (QECCs) codes and entanglement-assisted quantum error-correcting (EAQECCs) using Euclidean hulls and sums of cyclic codes of length n over a family of ring R-s=F-q+v(1)F(q)+v(2)Fq+<middle dot><middle dot><middle dot>+v(s)F(q )where q is an odd prime power and v(i)(2)=v(i), vivj=vjvi=0, for i,j=1,2,3,& ctdot;,s and i not equal j. The study delves into various aspects of this construction. We explore the generator polynomials, the dimension of both Euclidean hulls and the sums of cyclic codes over the ring R-s. Further, we determine several new QECCs and EAQECCs. This paper claims that our obtained codes have improved parameters (e.g. higher minimum distance or greater dimension) than the existing quantum codes. Moreover, we present some detailed examples that effectively illustrate our findings.
引用
收藏
页数：20
相关论文
共 50 条
  • [31] Codes and pseudo-geometric designs from the ternary m-sequences with Welch-type decimation d=2 <middle dot> 3(n-1)/2+1
    Xiang, Can
    Tang, Chunming
    Yan, Haode
    Guo, Min
    FINITE FIELDS AND THEIR APPLICATIONS, 2024, 94
  • [32] V3O7<middle dot>H2O as a Cathode Material for Aqueous Mg2+/Na+ Hybrid Electrochemical Cells
    Soellinger, Daniela
    Chen, Julie Lam
    Zalesak, Jakub
    Praxmair, Jakob
    Pokrant, Simone
    ACS OMEGA, 2025, 10 (10): : 10152 - 10161
  • [33] On quantum and LCD Codes Over The Ring Fq+vFq+v2Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_q+vF_q+v^2F_q$$\end{document}
    S. Ali
    G. Mohammad
    N. Jeelani
    P. Khan
    Quantum Information Processing, 21 (9)
  • [34] K0.39V2O5<middle dot>0.52H2O Nanostructures with Oxygen Vacancies as Cathodes for Aqueous Zinc-Ion Batteries
    Ba, Ying
    Yang, Guang
    Sun, Shuowen
    Zhang, Yue
    Jiang, Ruiting
    Sun, Juncai
    Liu, Wei
    ACS APPLIED NANO MATERIALS, 2025, 8 (02) : 1205 - 1213
  • [35] Enhanced field-effect mobility (&gt;250 cm2/V<middle dot>s) in GaN MOSFETs with deposited gate oxides via mist CVD
    Ikeyama, Kazuki
    Tomita, Hidemoto
    Harada, Sayaka
    Okawa, Takashi
    Liu, Li
    Kawaharamura, Toshiyuki
    Miyake, Hiroki
    Nagasato, Yoshitaka
    APPLIED PHYSICS EXPRESS, 2024, 17 (06)
  • [36] Constacyclic codes over the ring Fq+vFq+v2Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_q+v{\mathbb {F}}_q+v^{2}{\mathbb {F}}_q$$\end{document} and their applications of constructing new non-binary quantum codes
    Fanghui Ma
    Jian Gao
    Fang-Wei Fu
    Quantum Information Processing, 2018, 17 (6)
  • [37] Hermitian dual-containing constacyclic codes over Fq2+v1Fq2+⋯+vrFq2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{q^{2}}+{v_{1}}\mathbb {F}_{q^{2}}+\cdots +{v_{r}}\mathbb {F}_{q^{2}}$$\end{document} and new quantum codes
    Yu Wang
    Xiaoshan Kai
    Zhonghua Sun
    Shixin Zhu
    Cryptography and Communications, 2023, 15 (1) : 145 - 158
  • [38] Mg ions intercalated with V3O7<middle dot>H2O to construct ultrastable cathode materials for aqueous zinc-ion batteries
    Shi, Yaowen
    Yin, Bosi
    Sun, Ying
    Ge, Rongyuan
    Hu, Yingfang
    Li, Jiazhuo
    Li, Hui
    Zhang, Siwen
    Ma, Tianyi
    CHEMICAL COMMUNICATIONS, 2024, 60 (65) : 8597 - 8600
  • [39] Electrostatic adsorption driven self-assembly of V2O5<middle dot>4VO2 nanoribbons and MXene for fast and stable Zn2+ storage
    Zhou, Meng-Xuan
    Zhang, Shu-Chao
    Zou, Zheng-Guang
    Chen, Min
    Luo, Zhi-Hong
    Liang, Fang-An
    Zhong, Xi-Yuan
    Jia, Sheng-Kun
    Zhang, Wang-Ji
    RARE METALS, 2025, 44 (02) : 938 - 949
  • [40] Global health costs of ambient PM2<middle dot>5 from combustion sources: a modelling study supporting air pollution control strategies
    Yin, Hao
    Mcduffie, Erin E.
    Martin, Randall, V
    Brauer, Michael
    LANCET PLANETARY HEALTH, 2024, 8 (07): : e476 - e488
12345