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] Infinite families of MDR cyclic codes over Z4 via constacyclic codes over Z4[u]/⟨u2-1⟩
Han, Nayoung
Kim, Bohyun
Kim, Boran
Lee, Yoonjin
DISCRETE MATHEMATICS, 2020, 343 (03)
[42] Hamming and Symbol-Pair Distances of Constacyclic Codes of Length 2ps over R=Fpm[u,v]⟨u2,v2,uv-vu⟩
Acharya, Divya
Poojary, Prasanna
Bhatta, Vadiraja G. R.
SYMMETRY-BASEL, 2025, 17 (03):
[43] Some Constacyclic and Cyclic Codes Over Fq[u]/⟨ut+1⟩
Sobhani, Reza
Esmaeili, Morteza
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2010, E93A (04) : 808 - 813
[44] Cyclic codes and λ1 + λ2u + λ3v + λ4uv-constacyclic codes over Fp + uFp + vFp + uvFp
Zheng, Xiying
Kong, Bo
APPLIED MATHEMATICS AND COMPUTATION, 2017, 306 : 86 - 91
[45] On quantum and LCD Codes Over The Ring Fq + vFq + v2Fq
Ali, S.
Mohammad, G.
Jeelani
Khan, N.
Sharma, P.
QUANTUM INFORMATION PROCESSING, 2022, 21 (09)
[46] Quantum codes from cyclic codes over Fq + vFq + v2Fq + v3Fq
Gao, Jian
INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 2015, 13 (08)
[47] CYCLIC CODES OVER THE RING Fp[u, v, w]/⟨u2, v2, w2, uv - vu, vw - wv, uw - wu⟩
Kewat, Pramod Kumar
Kushwaha, Sarika
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2018, 55 (01) : 115 - 137
[48] Cyclic DNA codes over the ring F2[u]/u2-1) based on the deletion distance
Siap, Irfan
Abualrub, Taher
Ghrayeb, Ali
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2009, 346 (08): : 731 - 740
[49] Skew Cyclic Codes over Fq + vFq + v2Fq
Shi, Minjia
Yao, Ting
Alahmadi, Adel
Sole, Patrick
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2015, E98A (08) : 1845 - 1848
[50] Non-binary quantum codes from constacyclic codes over Fq[u1, u2, ..., uk]/⟨ui3 = ui, uiuj = ujui⟩
Kong, Bo
Zheng, Xiying
OPEN MATHEMATICS, 2022, 20 (01): : 1013 - 1020

← 1 2 3 4 5 →