Quantum codes from cyclic codes over Fq + uFq + vFq + uvFq

被引：68
作者：
Ashraf, Mohammad [1 ]
Mohammad, Ghulam [1 ]
机构：
[1] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India
来源：
QUANTUM INFORMATION PROCESSING | 2016年 / 15卷 / 10期
关键词：
Quantum codes; Cyclic codes; Self-orthogonal codes; Gray map; ERROR-CORRECTION; CONSTRUCTION;
D O I：
10.1007/s11128-016-1379-8
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, we study quantum codes over F-q from cyclic codes over F-q + uF(q) + vF(q) + uvF(q), where u(2) = u, v(2) = v, uv = vu, q = p(m), and p is an odd prime. We give the structure of cyclic codes over F-q + uF(q) + vF(q) + uvF(q) and obtain self-orthogonal codes over F-q as Gray images of linear and cyclic codes over F-q + uF(q) + vF(q) + uvF(q). In particular, we decompose a cyclic code over F-q + uF(q) + vF(q) + uvF(q) into four cyclic codes over F-q to determine the parameters of the corresponding quantum code.
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页码：4089 / 4098
页数：10
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