New MDS EAQECCs derived from constacyclic codes over Fq2+vFq2

被引：8

作者：

Gao, Jian ^{[1
]}

Zhang, Yaozong ^{[1
]}

Liu, Ying ^{[1
]}

Fu, Fang -Wei ^{[2
,3
]}

机构：

[1] Shandong Univ Technol, Sch Math & Stat, Zibo 255091, Peoples R China

[2] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

[3] Nankai Univ, Tianjin Key Lab Network & Data Secur Technol, LPMC, Tianjin 300071, Peoples R China

来源：

DISCRETE MATHEMATICS | 2023年 / 346卷 / 09期

基金：

中国国家自然科学基金;

关键词：

MDS EAQECCs; Defining sets; Constacyclic codes; Gray images; Finite non-chain rings; QUANTUM CODES;

D O I：

10.1016/j.disc.2023.113513

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Entanglement-assisted quantum error-correcting codes (EAQECCs) can improve information rate by using pre-shared entanglement between the sender and the receiver. In this paper, we construct three new infinite families of maximum distance separable (MDS) EAQECCs with less pre-shard maximally entangled states based on the Gray images of constacyclic codes over the finite non-chain ring Fq2 +vFq2 with v2 = v. The parameters of these MDS EAQECCs are not covered by the codes available in the previous literatures. Furthermore, our results generalize and improve the work of Lu et al. (2018) [16], (2020) [19]. (c) 2023 Elsevier B.V. All rights reserved.

引用

页数：12

共 29 条

[1] Correcting quantum errors with entanglement [J].

Brun, Todd ;

Devetak, Igor ;

Hsieh, Min-Hsiu .

SCIENCE, 2006, 314 (5798) :436-439

[2] Good quantum error-correcting codes exist [J].

Calderbank, AR ;

Shor, PW .

PHYSICAL REVIEW A, 1996, 54 (02) :1098-1105

[3] MDS Codes With Galois Hulls of Arbitrary Dimensions and the Related Entanglement-Assisted Quantum Error Correction [J].

Cao, Meng .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2021, 67 (12) :7964-7984

[4] Entanglement-assisted quantum MDS codes constructed from constacyclic codes [J].

Chen, Xiaojing ;

Zhu, Shixin ;

Kai, Xiaoshan .

QUANTUM INFORMATION PROCESSING, 2018, 17 (10)

[5]

Fan JH, 2016, QUANTUM INF COMPUT, V16, P423

[6] Euclidean and Hermitian Hulls of MDS Codes and Their Applications to EAQECCs [J].

Fang, Weijun ;

Fu, Fang-Wei ;

Li, Lanqiang ;

Zhu, Shixin .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2020, 66 (06) :3527-3537

[7] Quantum Codes Derived from Negacyclic Codes [J].

Gao, Jian ;

Wang, Yongkang .

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2018, 57 (03) :682-686

[8]

Gao J, 2018, QUANTUM INF PROCESS, V17, DOI 10.1007/s11128-017-1775-8

[9] Quantum codes from cyclic codes over Fq + vFq + v2Fq + v3Fq [J].

Gao, Jian .

INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 2015, 13 (08)

[10] Constructions of good entanglement-assisted quantum error correcting codes [J].

Guenda, Kenza ;

Jitman, Somphong ;

Gulliver, T. Aaron .

DESIGNS CODES AND CRYPTOGRAPHY, 2018, 86 (01) :121-136

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