On quantum codes obtained from cyclic codes over A2

被引：59

作者：

Dertli, Abdullah ^{[1
]}

Cengellenmis, Yasemin ^{[2
]}

Eren, Senol ^{[1
]}

机构：

[1] Ondokuz Mayis Univ, Dept Math, Fac Arts & Sci, Samsun, Turkey

[2] Trakya Univ, Fac Arts & Sci, Dept Math, Edirne, Turkey

来源：

INTERNATIONAL JOURNAL OF QUANTUM INFORMATION | 2015年 / 13卷 / 03期

关键词：

Quantum codes; cyclic codes; finite rings;

D O I：

10.1142/S0219749915500318

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, quantum codes from cyclic codes over A(2) = F-2 + uF(2) + vF(2) + uvF(2), u(2) = u, v(2) = v, uv = vu, for arbitrary length n have been constructed. It is shown that if C is self orthogonal over A(2), then so is Psi(C), where Psi is a Gray map. A necessary and sufficient condition for cyclic codes over A(2) that contains its dual has also been given. Finally, the parameters of quantum error correcting codes are obtained from cyclic codes over A(2).

引用

页数：9

共 9 条

[1] Quantum codes from cyclic codes over F3 + vF3
Ashraf, Mohammad
Mohammad, Ghulam
[J]. INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 2014, 12 (06)
[2] Quantum error correction via codes over GF (4)
Calderbank, AR
Rains, EM
Shor, PW
Sloane, NJA
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (04) : 1369 - 1387
[3] Codes over an infinite family of rings with a Gray map
Cengellenmis, Yasemin
Dertli, Abdullah
Dougherty, S. T.
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2014, 72 (03) : 559 - 580
[4] QUATERNARY CONSTRUCTION OF QUANTUM CODES FROM CYCLIC CODES OVER F4 + uF4
Kai, Xiaoshan
Zhu, Shixin
[J]. INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 2011, 9 (02) : 689 - 700
[5] Ma W, 2011, INT JOINT C IEEE TRU, V11
[6] Qian J., 2013, J INFORM COMPUTATION, V10, P1715, DOI DOI 10.12733/jics20101705
[7] QUANTUM CODES FROM CYCLIC CODES OVER FINITE RING
Qian, Jianfa
Ma, Wenping
Guo, Wangmei
[J]. INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 2009, 7 (06) : 1277 - 1283
[8] SCHEME FOR REDUCING DECOHERENCE IN QUANTUM COMPUTER MEMORY
SHOR, PW
[J]. PHYSICAL REVIEW A, 1995, 52 (04): : R2493 - R2496
[9] Simple quantum error-correcting codes
Steane, AM
[J]. PHYSICAL REVIEW A, 1996, 54 (06): : 4741 - 4751

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