Abstract

The purpose of this paper is to identify the structural characteristics and construction of quantum codes over $\mathcal{F}_p$ using $\alpha_1+\alpha_2 {\mu}+\alpha_3 {\nu}+\alpha_4 {\varpi}+\alpha_5 {\mu}{\nu}+\alpha_6 {\nu}{\varpi}+\alpha_7 {\mu}{\varpi}+\alpha_8 {\mu}{\nu}{\varpi}- $constacyclic codes over ring $\mathcal{R} ~= ~\mathcal{F}_p[{\mu},{\nu},{\varpi}]/<{\mu}^2-{\mu}, {\nu}^2-{\nu}, {\varpi}^2-{\varpi}~, {\mu}{\nu}-{\nu}{\mu}, {\nu}{\varpi}-{\varpi}{\nu}, {\mu}{\varpi}-{\varpi}{\mu}>$, here $\mathcal F_{p}$ is a finite field with p elements. We define a Gray map from $\mathcal{R}$ to $\mathcal{F}_p^{8}$, a distance-preserving map. Breaking down constacyclic codes into cyclic and negacyclic codes results in the creation of quantum codes over the finite field $\mathcal{F}_p$. As an application, some examples are illustrated to obtain the quantum codes of different parameters.

Keywords and Phrases

Gray map, cyclic codes, constacyclic codes, negacyclic codes.

A.M.S. subject classification

94B05, 94B15, 94B60.

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