NEW QUANTUM AND LCD CODES FROM CYCLIC CODES OVER A FINITE NON-CHAIN RING

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2023-04-01 DOI:10.1016/S0034-4877(23)00027-7

Nadeem ur Rehman, Mohd Azmi, Ghulam Mohammad

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引用次数: 0

Abstract

In this work, we study cyclic codes of length n over a finite commutative non-chain ring $ℛ = F_{q} [u, v] / 〈 u^{2} - γ u, v^{2} - ϵ v, u v - v u 〉$ where $γ, ϵ \in F_{q}^{*}$ and we find new and better quantum error-correcting codes than previously known quantum error correcting codes. Then certain constraints are imposed on the generator polynomials of cyclic codes, so these codes become linear complementary dual codes (in short LCD codes). We then verify that the Gray image of linear complementary dual codes of length n over $ℛ$ is a linear complementary dual code of length 4n over $F_{q}$ by establishing a Gray map.

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有限非链环上循环码的新量子码和LCD码

在这项工作中，我们研究了长度为n的循环码在一个有限交换非链环上的循环码=Fq[u,v]/ < u2−γu,v2−ϵv,uv−vu >，其中γ， λ∈Fq*，我们找到了比以前已知的量子纠错码更好的量子纠错码。然后对循环码的生成器多项式施加一定的约束，使这些循环码成为线性互补对偶码(简称LCD码)。然后，我们通过建立灰度图来验证长度为n / g的线性互补对偶码的灰度图像是长度为4n / g的线性互补对偶码。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.