Quantum codes from skew constacyclic codes over the ring Fq[u, v]/⟨u2-1, v2-1, uv - vu⟩

被引：31

作者：

Bag, Tushar ^{[1
]}

Dinh, Hai Q. ^{[2
,3
]}

Upadhyay, Ashish K. ^{[1
]}

Bandi, Ramakrishna ^{[4
]}

Yamaka, Woraphon ^{[5
]}

机构：

[1] Indian Inst Technol Patna, Dept Math, Patna 801103, Bihar, India

[2] Ton Duc Thang Univ, Inst Computat Sci, Div Computat Math & Engn, Ho Chi Minh City, Vietnam

[3] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

[4] Int Inst Informat Technol Naya Raipur, Dept Math, Atal Nagar 493661, India

[5] Chiang Mai Univ, Fac Econ, Ctr Excellence Econometr, Chiang Mai 52000, Thailand

来源：

DISCRETE MATHEMATICS | 2020年 / 343卷 / 03期

关键词：

Skew constacyclic codes; Dual codes; Quantum error-correcting codes; CYCLIC CODES; CONSTRUCTION;

D O I：

10.1016/j.disc.2019.111737

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study uantum error-correcting codes from skew constacyclic codes over the ring R = F-q[u, v]/< u(2) - 1, v(2) - 1, uv - vu >, where q = p(m) for any odd prime p and positive integer m. We decompose skew constacyclic codes over the ring R as a direct sum of skew constacyclic codes over F-q. Self-dual skew constacyclic codes over the ring R are characterized. Necessary and sufficient conditions for skew negacyclic and skew constacyclic codes to be dual-containing are obtained. As an application, we construct new quantum error-correcting codes from skew constacyclic codes over F-q. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：17

共 50 条

[41] (1-2u3)-constacyclic codes and quadratic residue codes over Fp[u]/⟨u4 - u⟩
Raka, Madhu
Kathuria, Leetika
Goyal, Mokshi
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2017, 9 (04): : 459 - 473
[42] (1+λu)-Constacyclic codes over Fp[u]/⟨um⟩
Kai, Xiaoshan
Zhu, Shixin
Li, Ping
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2010, 347 (05): : 751 - 762
[43] Quantum and LCD codes from skew constacyclic codes over a finite non-chain ring
Prakash, Om
Verma, Ram Krishna
Singh, Ashutosh
QUANTUM INFORMATION PROCESSING, 2023, 22 (05)
[44] (1 - 2u(2))-Constacyclic Codes over F-p
Mostafanasab, Hojjat
Karimi, Negin
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2016, 9 (01): : 39 - 47
[45] On reversible DNA codes over the ring Z4[u,v]/⟨u2-2,uv-2,v2,2u,2v⟩based on the deletion distance
Dinh, Hai Q.
Ashraf, Mohammad
Rehman, Washiqur
Mohammad, Ghulam
Asim, Mohd
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2024,
[46] A class of constacyclic codes over Fpm [u]/⟨u2⟩
Rani, Saroj
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2022, 53 (02) : 355 - 371
[47] Quantum codes from Hermitian dual-containing constacyclic codes over Fq2 + vFq2
Wang, Yu
Kai, Xiaoshan
Sun, Zhonghua
Zhu, Shixin
QUANTUM INFORMATION PROCESSING, 2021, 20 (03)
[48] A Family of Constacyclic Codes over ?2m plus u?2m and Its Application to Quantum Codes
Tang, Yongsheng
Yao, Ting
Zhu, Shixin
Kai, Xiaoshan
CHINESE JOURNAL OF ELECTRONICS, 2020, 29 (01) : 114 - 121
[49] m-ADIC RESIDUE CODES OVER THE RING Fq[v]/(vs - v) AND THEIR APPLICATIONS TO QUANTUM CODES
Kuruz, Ferhat
Sari, Mustafa
Koroglu, Mehmet E.
QUANTUM INFORMATION & COMPUTATION, 2022, 22 (5-6) : 427 - 439
[50] Constacyclic codes over the ring F2+uF2+u2F2
Ding, Jian
Li, Hong-Ju
Zuo, Xue-Wu
Liang, Jing
Tien Tzu Hsueh Pao/Acta Electronica Sinica, 2015, 43 (01): : 145 - 150

← 1 2 3 4 5 →