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On quantum codes obtained from cyclic codes over $𝔽_{2} + u 𝔽_{2} + u^{2} 𝔽_{2}$

Abhay Kumar Singh

Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, Jharkhand 826004, India

E-mail Address: singh.ak.am@ismdhanbad.ac.in

Corresponding author.

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Sukhamoy Pattanayak

Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, Jharkhand 826004, India

E-mail Address: sukhamoy88@gmail.com

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Pratyush Kumar

Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, Jharkhand 826004, India

E-mail Address: vikey397@gmail.com

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, and

Kar Ping Shum

Institute of Mathematics, Yunnan University Kunming, Kunming, Yunnan 650091, P. R. China

E-mail Address: kpshum@ynu.edu.cn

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https://doi.org/10.1142/S1793557118500092Cited by:13 (Source: Crossref)

Abstract

In the paper, we consider a finite non-chain commutative ring $R = 𝔽_{2} + u 𝔽_{2} + u^{2} 𝔽_{2}$ , where $u^{3} = u$ . We mainly study the construction of quantum codes from cyclic codes over $R$ . For this, we obtained self-orthogonal codes over $𝔽_{2}$ as gray images of linear and cyclic codes over $R$ , then these codes over $𝔽_{2}$ correspond to a cyclic code over $R$ of odd length $n$ used to determine the parameters of the quantum codes.

Communicated by B. K. Dass

Keywords:

AMSC: 94B15

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