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
AMS Subject Classification
94B05, 94B15, 94B60.
How to Cite
Rekha Kumawat, Monika Sangwan (2025). QUANTUM CODES THROUGH CONSTACYCLIC CODES OVER $\mathcal{F}_{p}+{\mu}\mathcal{F}_{p}+{\nu}\mathcal{F}_{p}+{\varpi}\mathcal{F}_{p}+{\mu}{\nu}\mathcal{F}_{p}+{\nu}{\varpi}\mathcal{F}_{p}+{\mu}{\varpi}\ma. South East Asian Journal of Mathematics and Mathematical Sciences, 21(3), 349-360.