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arXiv:1601.02328

On Quantum Codes Obtained From Cyclic Codes Over $\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$

Sukhamoy Pattanayak, Abhay Kumar Singh, Pratyush Kumar

Published Jan 11, 2016• 0 citations
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Abstract

Let $R=\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$ be a non-chain finite commutative ring, where $u^3=u$. In this paper, we mainly study the construction of quantum codes from cyclic codes over $R$. We obtained self-orthogonal codes over $\mathbb{F}_2$ as gray images of linear and cyclic codes over $R$. The parameters of quantum codes which are obtained from cyclic code over $R$ are discussed.

DOI
10.48550/arxiv.1601.02328

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On Quantum Codes Obtained From Cyclic Codes Over F2+uF2+u2F2\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2F2​+uF2​+u2F2​
Let R=F2+uF2+u2F2R=\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2R=F2​+uF2​+u2F2​ be a non-chain finite commutative ring, where u3=uu^3=uu3=u. In this paper, we mainly study the construction of quantum codes from cyclic codes over RRR. We obtained self-orthogonal codes over F2\mathbb{F}_2F2​ as gray images of linear and cyclic codes over RRR. The parameters of quantum codes which are obtained from cyclic code over RRR are discussed.
In the paper, we consider a finite non-chain commutative ring [Formula: see text], where [Formula: see text]. We mainly study the construction of quantum codes from cyclic codes over [Formula: see text]. For this, we obtained self-orthogonal codes over [Formula: see text] as gray images of linear and cyclic codes over [Formula: see text], then these codes over [Formula: see text] correspond to a cyclic code over [Formula: see text] of odd length [Formula: see text] used to determine the parameters of the quantum codes.