A study of quantum codes obtained from cyclic codes over a non-chain ring

被引：2
|
作者：
Dinh, Hai Q. [1 ]
Kumar, Narendra [2 ]
Singh, Abhay Kumar [3 ]
机构：
[1] Kent State Univ, Dept Math Sci, 4314 Mahoning Ave, Warren, OH 44483 USA
[2] Indian Inst Sci Bangalore, Dept Elect Commun Engn, Bangalore 560012, Karnataka, India
[3] Indian Inst Technol ISM, Dept Math & Comp, Dhanbad 826004, Bihar, India
来源：
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2022年 / 14卷 / 04期
关键词：
Cyclic codes; Quantum codes; Gray map;
D O I：
10.1007/s12095-022-00567-6
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper, the structure of cyclic codes of odd length n over R = Z(4) + vZ(4), v(2) = v, is conferred. We define a Gray map xi, which is distance preserving from Rn (Gray distance) to Z(2)(4n) (Hamming distance), and show that it is Z(2)-linear. We construct quantum codes over Z(2) by utilizing the Gray images xi (C) of cyclic codes C over R. As an application, we provide many new quantum MDS codes and quantum codes with good parameters comparing to known quantum codes.
引用
收藏
页码：909 / 923
页数：15
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