Quantum codes from (1-2u1-2u2 - ...-2um)-skew constacyclic codes over the ring Fq + u1Fq + ... + u2mFq

被引：0

作者：

Bag, Tushar ^{[1
]}

Ashraf, Mohammad ^{[2
]}

Mohammad, Ghulam ^{[2
]}

Upadhyay, Ashish K. ^{[1
]}

机构：

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

[2] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India

来源：

QUANTUM INFORMATION PROCESSING | 2019年 / 18卷 / 09期

关键词：

Linear codes; Gray map; Skew constacyclic codes; Quantum codes; CYCLIC CODES; ERROR-CORRECTION; CONSTRUCTION;

D O I：

10.1007/s11128-019-2384-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we study a class of skew constacyclic codes over the ring R = F-q + u(1)F(q)+ ... + u(2m) F-q, where u(i)(2) = u(i), u(i)u(j) = u(j)u(i) = 0, for i, j = 1, 2,..., 2m, i not equal j and q = p(s), and derive the generator polynomials of this class of codes over R. Also, by using Calderbank-Shor-Steane construction, some new non-binary quantum codes have been obtained. Moreover, new quantum codes [[225, 201, 5]](9), [[351, 333, 4]](9), [[405, 393, 3]](9), [[405, 381, 5]](9) have been constructed.

引用

页数：15

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[10] Quantum codes from (1-2u1-2u2-⋯-2um)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1-2u_1-2u_2-\cdots -2u_m)$$\end{document}-skew constacyclic codes over the ring Fq+u1Fq+⋯+u2mFq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_q+u_1F_{q}+\cdots +u_{2m}F_{q}$$\end{document}
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