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Asian-European Journal of Mathematics

On quantum codes obtained from cyclic codes over 𝔽2 + u𝔽2 + u2𝔽2

Abhay Kumar Singh, Sukhamoy Pattanayak, Pratyush Kumar, K. P. Shum

Published Feb 17, 2017• 13 citations
Publisher

Abstract

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.

DOI
10.1142/s1793557118500092

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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.
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.
QUATERNARY CONSTRUCTION OF QUANTUM CODES FROM CYCLIC CODES OVER F4+uF4\mathbb{F}_4 + u\mathbb{F}_4F4​+uF4​